That's all from us for today's coverage of the Women's World Cup but there will be plenty of reaction and previews on the BBC Sport website today, and I'll leave you with the highlights of today's two games below.

Republic of Ireland boss Vera Pauw: "It is very disappointing. We said at half time it would be a game decided by one mistake, whether it was us or them, and that is what happened.

"Sam Kerr is one of the major top strikers of the world so her not playing was of course an advantage for us. They have such a powerful team, it was difficult for us to play against them but they did so well. They didn't create a lot of chances, right?

"A draw would have been a reasonable result. I think everybody is proud that we are part of the top nations and we can only grow from this."

Australia boss Tony Gustavsson: "We knew this game would be tough. All the teams here will put up a fight. Everyone can beat everyone in this tournament. We knew set pieces would be a massive part of it and I have to credit the team for how they handled all those set plays in the final stages. They are one of the best teams in attack on set plays and we dealt with it.

"Tournament football is always about finding a way to win. There's been a lot challenges thrown at this team over the last 24 hours, an opening game at a home World Cup and then you add Sam Kerr's injury to that. They stuck together and played as a team and that mental toughness I am proud of.

"The fans carried this team to the victory. That support was amazing. In the stands they were amazing."

On Sam Kerr injury: "This is her dream, she has been planning and preparing for it for years. This is her big moment to step up as captain and play in front of her fans and friends and family. It is devastating but the way she spoke to the team today says a lot about her as a person and as a captain for this team."

A busier day tomorrow with three games coming up:

03:30 BST:

Nigeria v Canada (BBC)

06:00 BST:

Philippines v Switzerland (ITV)

08:30 BST:

Spain v Costa Rica (BBC)

Former Republic of Ireland forward Olivia O'Toole speaking to ITV 1: "The girls should have got something from the game, Australia had one chance in the game. It was given as a penalty, to me it wasn't. I'm absolutely 100% so proud of the girls, so proud. They did our little country proud.

"I didn't agree with Vera Pauw's decisions, I thought Amber Barrett would have made a difference today.

"We need something from the Canada game to carry on to Nigeria."

On what Republic of Ireland need to improve: "They had passion, they were composed. Six or seven corners at the end of the game, two chances. They just need to go home look at what they did in the second half and get a result against Canada."

Emma Byrne
Former Ireland goalkeeper speaking on ITV1

It's a very, very important win for Australia.

They're not normally very good in their opening games at World Cups, they've lost their last three.

They didn't really show much to be honest, they didn't have a plan B, or create an awful lot either.

So for them to walk away with the three points is great for them.

Republic of Ireland captain Katie McCabe speaking to ITV 1: "Little [Abbie] Larkin and Lucy [Quinn] coming on brought a bit of energy. The Aussies were tiring towards the end and we gave a good account of ourselves in the second half and we have things to build on for the second game against Canada.

"I enjoyed the physical game, I think everyone enjoyed it. We said earlier in the week that we don't shy away from that. We love the physicality and it was an enjoyable game."

Image source, Getty Images

Australia stand-in captain Steph Catley speaking to ITV 1: "It's hard to put into words to be honest. It's been such a big build up for us. We've had a lot of adrenanaline and excitement coming into the game, we had some moments where we had to work through that.

On scoring the winning goal from the penalty spot: "Obviously we didn't have Sammy tonight [Sam Kerr]. I've had conversations with Tony about it, about me potentially needing to take one if the opportunity came up, and I felt confident to do it. I've been practicing a lot recently and was happy to take it. For it to be my first World Cup goal was really special."

Emma Byrne
Former Ireland goalkeeper speaking on ITV1

There's no complaints to be had about the penalty decision.

It was a silly one for Ireland to give away because they had done really well to keep Australia at bay, defended very, very well.

Sadly it has cost them.

With captain Sam Kerr ruled out of Australia's first two group games with a calf injury, it felt imperative they got a win today. Now there's a little bit less pressure on them going into their next game against Nigeria on Thursday, 27 July. Kerr will also miss that game but could be back for their final group fixture against Canada on Monday, 31 July.

Karen Bardsley
Former England and Manchester City goalkeeper on BBC Radio 5 Live

It certainly was an interesting game.

Lots of transitional moments. Strong possession play from Australia, and plenty of dominance.

Some shows of confidence from Ireland, hey managed to create plenty of chances but just couldn't find the quality to get on the scoresheet.

They put up a great fight and matched Australia player for player up and down the pitch, and pushed them to the very last.

Image source, Getty Images

Emma Smith
BBC Sport reporter at Stadium Australia, Sydney

At Euro 2022, England started with a scrappy 1-0 win but improved and went on to win the tournament as hosts.

At the 2023 World Cup, could Australia do the same?

All over! Australia hold on to ensure they kick off this home World Cup with a win.

It was not to be for the Republic of Ireland, but they produced a hugely encouraging performance and leave the field with their heads held high.

Image source, BBC Sport

Big chance!

Abbie Larkin is suddenly in behind, she finds Katie McCabe, who stabs a shot at goal that Mackenzie Arnold fumbles before the ball is scrambled away.

Karen Bardsley
Former England and Manchester City goalkeeper on BBC Radio 5 Live

You can feel the pressure.

Australia are maintaining the authority in this game if you will but the Irish are pressing very high.

This injury stoppage should give them a chance to reset and see it out.

Into the final minute. Time is about to run out for the Republic of Ireland but whatever the result they have put in a really encouraging, battling performance here.

Katie Smith
BBC reporter in Melbourne

It's been a rainy evening in Melbourne but fans have turned out in their droves to watch Australia on the big screen in Federation Square.

They're getting stuck into the game and it's a majority male crowd too. I’ve spotted a couple of Irish flags but 99% green and gold here.

Image source, BBC Sport

Karen Bardsley
Former England and Manchester City goalkeeper on BBC Radio 5 Live

Absolutely crucial.

A big left hand from Arnold emerging from the crowd to paw away that corner from Connelly.

Really great effort, she's coming up clutch for her side.

Image source, Getty Images

Nothing comes of the latest corner but the Republic of Ireland keep up the pressure, Abbie Larkin this time lashing over.

It is another awkward delivery but Mackenzie Arnold comes to the rescue again and the ball is put out for yet another corner.

Australia are under pressure.