The Barclays Premier League champions drew 2-2 with Liverpool at the Etihad Stadium on Sunday, their second draw in the space of five days. That meant another two points dropped and they now trail rivals Manchester United by nine at the top of the table, four more than a week ago.
But manager Roberto Mancini was quick to insist the title race was not over and Hart maintains the players will remain confident, saying: "We have got to be. There is no point turning up otherwise. We have got to win every game and look not to drop any points. It is a good challenge for us."
He added: "We will always be in it, but unfortunately it's a big gap, getting too big for our liking. You have to move forward, and that means we have to beat Southampton next week. We are nine points behind with 13 games to go, so we need the win."
City claimed a point from a pulsating match when Sergio Aguero sensationally rounded Jose Reina and chipped home from an outrageous angle 12 minutes from time.
That cancelled out an equally stunning long-range strike from Liverpool captain Steven Gerrard which had put the Reds ahead five minutes earlier.
Edin Dzeko and former City striker Daniel Sturridge, the latter in controversial circumstances, traded goals in the first half.
City were unhappy Daniel Agger was not penalised for a foul on Dzeko, and that Liverpool did not put the ball out of play as the Bosnian lay injured in the build-up to Sturridge's equaliser.
Hart, 25, said: "It was a tough game. I thought Liverpool played really well. I imagine they'll argue we were lucky to get a result in the end. That's a shame but you have got to move forward. They are a good side and I think they have finally worked out what the manager wants from them.
"They are a really tough side to play against. It is not the result we wanted but I think a draw is a fair result."