The 24-year-old believes his side made up for their "utterly disappointing" FA Cup exit last weekend, while stand-in captain Leon Osman also expressed his delight with the victory
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And Coleman says the win achieved Everton's aim of repaying the home faithful after they were dumped out of the cup by the Latics.
“It was utterly disappointing to go out [of the FA Cup],” Coleman told Sky Sports. “We went out there today and tried to repay the fans and I think we did that.
“That was what we came to do. Winning games is what we're about. It wasn't the Everton team last week, we just didn't turn up.”
Everton took the lead thanks to a 30-yard strike from stand-in captain Osman and the 31-year-old expressed his delight with his side’s victory, although he admitted it was difficult to grind out a result against the Premier League champions.
“Joe [Hart] is a fantastic keeper, to beat him from that range, I'm delighted," he said.
“It went in the back of the net and it gave us the goal we needed to try and win the match.
“Difficult to play with 10 against any team, let alone the champions. But we kept them at bay and I don't think they had many chances.
“It's what we've got to concentrate on. We're trying to get up as high as we can.”