While Manchester United claimed a late victory over Newcastle United, City were beaten 1-0 by Sunderland to slip seven points behind their rivals at the top of the table.
Hart concedes that the situation is far from ideal but insists there is pressure on United as well as City.
"We've had leads, United have had the lead - it's to-ing and fro-ing at the moment," he said on the club's official website.
"We're a team of winners, it's hard and it hurts but we've got to move on. It is hard to lead and it is hard to chase too.
"We've clawed points back before, we proved it at the end of last year - we've just got to believe."
Adam Johnson scored the only goal of the game for Sunderland to extend City's poor recent record at the Stadium of Light, and Hart was disappointed to let the ball squirm past him at the near post.
He added: "First and foremost someone stamped on Zaba - it was a blatantly obvious foul but what can you do?
"A few of our players have stopped but Johnno has seen me sniffing for a cross and he's struck it well with that stiff ankle of his and it just deviated under my hand unfortunately."
"The only way we can change it is (City's record at Sunderland) by winning here next year but for now we only have Norwich on our minds.
"Simon Mignolet has had a magnificent game, he's a brilliant goalkeeper. I've watched him closely in other games and I think Sunderland defended for their lives and it just wouldn't go in for us."