The result was much needed after last week's FA Cup collapse at home to Wigan Athletic.
Coleman said: "It's what we aimed to do. Ultimately disappointing to go out of the FA Cup. We went out there and tried to repay the fans as much we could and I think we did that.
"Winning games is what it's all about and it's never nice to lose games, especially when we thought we could do well in the FA Cup this year.
"But we still have a lot to play for in the league and we showed it there today.
"That wasn't the Everton team last week, we just didn't turn up.
"Going down to 10 men we just worked as hard as we could. We're all mates here and I think that showed."