City suffered another setback in their quest to retain the Barclays Premier League title as they were held to a 2-2 draw with Liverpool on Sunday.
That result came five days after a goalless stalemate at struggling QPR and City now find themselves trailing rivals Manchester United by nine points at the top of the table.
Just a week ago the gap had been five points but Hart insists spirits have not dropped.
The 25-year-old England number one said: "Of course we still feel we can do this. That's who we are, and that's what we are.
"We've put ourselves in a worse position than we would like to be, but that's football sometimes."
City memorably overturned an eight-point deficit with just six games remaining to pip United to the crown on goal difference last season. The turning point then came after a damaging defeat at Arsenal in April.
Manager Roberto Mancini publicly wrote off his side's hopes but privately the squad steeled themselves for one last determined push. Yet Hart played down any comparisons between the situation then and now.
He said: "We do that anyway. It's not like we just float along and think, 'Oh my God, we're six points behind, we're nine points behind, we had better talk to each other'.
"The same stuff goes on - there is stuff we need to address and that gets done on a regular basis."