Hart is already set for the next challenge after Wayne Rooney's wonder goal gave Manchester United a 2-1 victory at Old Trafford on Saturday. City midfielder David Silva cancelled out Nani's opener, only for the England striker to have the last word.
Hart said: "It's deflated us a bit, but you've got to pick yourselves up and move on.
"You can't give up. If you're going to do that then there's no point in turning up every week. We are here to win games, do well for Manchester City and push the club on. That's not changed. We are still in the hunt for trophies, and we want to make it happen. The derby has gone.
"It's unfortunate that we lost, but we have to brush ourselves down and carry on. We've got the Europa League and the FA Cup as well as the Premier League to focus on.
"We know what we are about. People have been talking about Manchester United all season, but we played well. It's just a shame that we couldn't produce that bit of magic."