The former Red Devil believes that a 4-4 draw turned the tide in City's favour last season as he looks to extend a run of never losing a Premier League game which he has started
The Republic of Ireland international has become a permanent fixture in David Moyes side following a move to Goodison Park in January, having failed to establish himself at Old Trafford.
Shortly after his arrival, he travelled back to Manchester to help his new team snatch a point in a thrilling 4-4 draw, coming back from 4-2 down, which he feels hamstrung their bid for glory, and the two sides meet in their season opener on Monday night to play out a revenge match.
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"They try to win every game but maybe there is a bit of anger there because the game against us lost them the league really, but we will go out and try and get the right result.
"They would have been wounded to lose the title to anyone but especially losing it to the noisy neighbours as they are known."
Gibson is now happy that he has had a full pre-season and is raring to go as he looks to continue his outstanding record of being unbeaten in every Premier League game that he has started for both United and Everton.
He added: "Pre-season has gone really well. In terms of results it has not been exciting but the squad as a whole, everyone is fit, and we are all looking forward to the first game.
"I had a thigh strain but it is okay now so I am just going to prepare for the next few days and everyone is ready to go now.
"It is the first pre-season where I have come back really excited because I know I have a good chance of playing in nearly every game so I really hope it goes well.
"I just want to play as many games as possible, stay fit, score more goals – everything really. I am just looking forward to the first proper season of my career."