City clinched the narrow win thanks to a Vincent Kompany header moments before half-time and they now sit at the top of the Premier League on goal difference. Hart is adamant their league position is nothing more than they deserve, adding that although they do not want to get carried away, they have to enjoy times like these.
"We deserve to be in the position we are in - we are a good team, with good players and good fans and we are going places," Hart told reporters.
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"There is no point in being robots. You have to feel that vibe and we felt the fans."
Although City are in the driving seat for the Premier League title, Hart knows they are not on the home straight yet, highlighting the difficulty they could face when they travel to Newcastle on Sunday.
He added: "We were pleased to win but we have moved on.
"It's all about Newcastle now, which is pretty similar to what happened earlier in the season when we won at United - it was a great feeling but then we had the next game.
"It's all very well winning one game. But you can't just win one game if you want to do well. You need to win every one.
"Now we go to Newcastle to face a very tough side in a tough stadium, hoping we can get a good result."