The Killybegs footballer helped launch wave after wave of attack on a United side rapidly losing its gloss.
Coleman paid tribute to new Everton boss Roberto Martinez afterwards as the blues secured their first victory at Old Trafford in 21 years.
Brian Oviedo scored four minutes from time to give Everton the win.
“It’s been too long really and the manager has been working hard to get us to believe we could come here and get a result,” he said.
“It came on the way we’ve been playing, the way we’ve been keeping the ball and the confidence that has built. He just wanted us to play with no fear.
“Earlier in the season we tried to go to City in the same way but since then the manager has had more time to instil belief in us and we’re delighted with the result.
“From the sidelines all we could hear was the manager telling us to keep getting on the ball, and that was when we were 1-0 up.
“We got a brilliant result against Stoke and worked hard in training on how to beat United. Thankfully we did.”
He said Everton can do well this season.
“Without a doubt it makes us think the top four is possible,” he said. “Coming to places like this and getting a result the way we’re playing makes us think we can finish high up the table.
“This will only give us more confidence. We know we’ve to Arsenal next and they’re top but we’re looking forward to it, just like we were looking forward to this. We’ve got some good points from some tough games.”
Coleman also saluted fellow full-back Bryan Oviedo for his goal.
“He’s done fantastically,” he added. “It’s a blow to be missing Leighton because he’s one of the best there is but we’re happy for Bryan. He’s such a likeable character and as you see when he scores we all have a lot of time for him.
“He’s waited a long time for his chance and he deserves it. It was going to have to be an injury because of the way Bainesy plays but he’s taken his chance. I’m sure he’s delighted.”
Meanwhile Shay Given was unlucky not to have helped his new side Middlesbrough to a point at Derby.
Despite being down to 10 men for most of the game Boro looked as if they were heading for a 1-1 draw with the Rams.
But in the 90th minute former Derry City striker Connor Sammon popped up to give Derby all three points.