As well as chasing a fifth successive league title, Chelsea hope to have success in both domestic cups and the Champions League this season.
Managing an injury-hit squad will be crucial and knowing they had one foot in the last four, Hayes made seven changes to the starting 11 at Stamford Bridge.
"I’m happy for Ramirez, [making her European] debut. She was really excited. It gives me selection headaches for the weekend," said Hayes.
"When you make so many changes you have to expect disruption both sides of the ball.
"In the second half, for sure, they had to go for it. We relaxed a little bit, it was too transitional - but we’re through so I have to focus on that."
Among those to keep her place was 20-year-old Aggie Beever-Jones and the winger was hugely impressive just 24 hours after missing out on England senior squad selection.
She teed up Erin Cuthbert, Guro Reiten and Ramirez in the first half, before the Colombian forward, the British record signing, coolly gave Chelsea the lead when played through on goal.
Cuthbert was another standout performer, picking up the player of the match award and receiving praise from Ajax captain Sherida Spitse.
“I love football and watching football. I saw, for example today, Erin Cuthbert and how she is playing," said Spitse.
"I’m walking around the pitch with a smile on my face because of how she is playing. Of course she is our opponent but how she is playing is nice.
"And how we played against them... I’m really proud of my own team."
Ajax did not whimper out of the competition - Romee Leuchter and Tiny Hoekstra almost broke the deadlock in the first half.
Musovic was forced into two acrobatic diving saves to deny Leuchter and substitute Danique Tolhoek later on.
Those chances will no doubt infuriate Hayes but this was all about progressing to the semi-finals which Chelsea did with relative ease across the two legs.
They have an FA Cup semi-final to play next month as well as this weekend’s League Cup final and Chelsea have once again proven their pedigree in European competition.