Manchester City 3-1 Everton (agg 4-3)

Sergio Aguero scores one of the most important goals of Manchester City's season

Manchester City clawed back a first-leg deficit to beat Everton and set up a Capital One Cup final date with Liverpool after a thrilling game at the Etihad.

Everton looked on course for Wembley when Ross Barkley's brilliant run and 20-yard shot added to their 2-1 advantage from the first leg in the 18th minute - but manager Roberto Martinez was left nursing a burning sense of injustice after an enthralling encounter turned on a controversial decision.

Fernandinho's deflected shot put City level on the night before the break but Everton still had the edge. That was until City substitute Kevin de Bruyne, who was later taken off with a serious-looking knee injury, turned home Raheem Sterling's cross with 20 minutes left.

Everton could not recover their composure and City, who had earlier hit the woodwork through Sergio Aguero and David Silva, sealed their place in the final on 28 February when the Argentine headed De Bruyne's cross beyond keeper Joel Robles.

It meant joy for City and bitter disappoint tinged with fury for Martinez and Everton.

Relive the action as it happened from the Etihad Stadium

BBC 5 live in short: Man City beat Everton to reach League Cup final

BBC 5 live daily podcast: 'Man City can win treble'

Everton suffer injustice

This was arguably the biggest game of Roberto Martinez's reign as Everton manager, and a chance to silence criticism of his methods by setting up a League Cup final meeting with Merseyside rivals Liverpool.

And for 70 minutes Martinez and his team looked likely to pull it off, impressively standing toe-to-toe with City with a mixture of defensive solidity and threat on the break.

It was all turned on its head in a moment that will haunt and anger Martinez, as Sterling appeared to have run the ball out of play before crossing for De Bruyne to switch momentum decisively in City's favour.

The home side will not have sympathy for Everton in this context after being convinced Ramiro Funes Mori scored an offside goal in the first leg and that Jesus Navas was denied a penalty after he was fouled by Kevin Mirallas - but it was easy to understand Martinez's outspoken frustration.

City were increasing the pressure but Everton were surviving, with some good fortune, and that second goal stunned Martinez's team and gave the home side the push they needed to finally see Everton off.

Once more Everton never looked fully secure at the back but they certainly had a hard luck story to tell here.

Good news, bad news for Man City

Manchester City can now plan for a Wembley date with Liverpool, who beat them so comfortably 4-1 here at the Etihad earlier this season - but it was a night of mixed news for manager Manuel Pellegrini.

Aguero, whose season has been hampered by injuries, looked back to his blistering best and never gave Everton's defence a moment's peace, hitting the post with a superb curling effort then showing his world-class by heading in De Bruyne's cross for the goal that clinched City's victory.

The bad news is that injury to the brilliant De Bruyne, who had a huge impact after coming on as sub, scoring that controversial second and setting up the third.

The sight of the 24-year-old being taken off with his knee in a brace put a dampener on an exhilarating night and City will wait anxiously for the medical bulletin.

Barkley shows his class

Everton manager Roberto Martinez: "It's very, very hard to take"

Ross Barkley's run and finish that put Everton ahead in the 18th minute was more compelling evidence of a wonderful natural talent.

City simply could not cope with his movement and power when Everton had moments of superiority in the first half, and it was no coincidence that their effectiveness was reduced once he was subdued.

Barkley is occasionally the target for harsh criticism from a minority of Everton's fans, which sometimes subdues his sense of adventure - but it is clear they have a special player on their hands.

On a night of bitter disappointment for Everton, they can be consoled by the presence of the likes of Barkley, a player they must build around and secure for the future.

Man of the match - Sergio Aguero (Manchester City)

The Argentina striker has a habit of scoring on big occasions - he scored his 16th of the season, and arguably the most important so far

What the managers said

Everton manager Roberto Martinez on BBC Radio 5 live: "Everyone that has seen the replay can clearly see the ball is out of play when the ball is crossed in for City's second goal. The tie was a real good football game. You don't expect to concede a goal in that manner. It's very, very hard to take.

"City are a very good side. If they score three goals in the right way then you accept it. The first goal was a deflected shot, but for the second goal the ball was clearly out.

"We have a very good group of young players. I hope we take this display as inspiration."

City manager Manuel Pellegrini: "I am very happy to play a final at Wembley, it is very important.

"We deserved to be in the final, we had just one defeat - that was against Everton with a clear penalty.

"They scored for 1-0 and it was a clear foul. If you think because of that ball [Sterling to de Bruyne], that is not why we won.

"We won because we scored three goals and Everton had just one chance."

The stats you need to know

• Manchester City will now play in a major final for the fourth time in the past six seasons

• Sergio Aguero has scored five goals in his past three games for City in all competitions

• De Bruyne has scored five goals in five appearances in the League Cup this season, including at least one in every round

• City have found the back of the net in all but one of their past 27 home games in all competitions

What next

City are away at Aston Villa in the FA Cup fourth round on Saturday, and Everton are at Carlisle in the same competition on Sunday.