The deficit emerged following a defeat by Sunderland courtesy of a goal from former midfielder Adam Johnson and Chicharito's late winner against Newcastle.
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City managed to overhaul an eight-point gap set by their neighbours late last season to win their first league title since 1968.
Chelsea are also within four points of Roberto Mancini's men with a game in hand, but Hart is only looking upwards - and more importantly - at regaining the title.
He told reporters: "We’ve had leads, United have had the lead — it’s to-ing and fro-ing at the moment.
"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.
"We’ve clawed points back before — we proved it at the end of last season. We’ve just got to believe."