The left-back scored City’s first, only his second goal for the club, before Aleix Garcia doubled the lead. Gylfi Sigurdsson’s late goal proved only to be a consolation as the Blues made it through the fourth round.
After nine changes from the weekend victory over Bournemouth, Clichy insists the aim of the evening was simply to reach the fourth round where they will now face Manchester United.
He said: “We could have avoided the goal as in England you never know until the final whistle. Overall we controlled the game but we didn’t start well. The first half wasn’t good enough but then we started to play in the second half.
“The victory is the most important thing though because if you lose you are out of the competition so now we can rest and look forward to Saturday.”
The Frenchman’s goal came after a fantastic move that started all the way back with Willy Caballero in City’s goal and he acknowledged how crucial it was for the Blues to get ahead.
“It just happens sometimes there is a moment in the game where the game changes a little bit,” said Clichy.
“The first half wasn’t good enough but in the second half we came back with more desire so we have to keep playing like this. It was a good night for everybody including the young players and everyone is happy now.”
As well as man of the match Garcia, fellow youngsters Angelino and Tosin Adarabioyo both featured in the victory.
“The academy provides some good players like we’ve seen tonight. It was nice to see the young players and it’s good for the fans to see the future of the club,” said Clichy.
There was one sour note for the Blues after Vincent Kompany went straight down the tunnel moments before the final whistle, despite an imperious return after four months since his last start.
Clichy, however, is hopeful that the signs are good for City’s skipper.
He said: “Most of the time when you come back after a long period you don’t play for more than an hour so I think he was probably just a bit tired and hopefully it will just be a matter of days.
“Vincent is Vincent. Fully fit he’s one of the best centre halves in Europe and we all know his quality. We’ve played well so far but having someone like him is a real bonus.”