Hart thinks that City will respond quickly and guard against complacency in the league with a squad full of players fighting to play in next month's Wembley showpiece.
He told The Sun: "It feels disappointing but we will be able to assess the bigger picture at a later date.
"Now we have a Cup final to look forward to and, after that, a summer of getting our heads down and sorting it out for next year. We will bounce back easily, it's what we do.
"We've another big game coming up at the weekend against West Ham and then have the FA Cup final, and all the lads are trying to get their spots for it."
City return to Premier League action and a fight to secure second place on Saturday at home to West Ham United.