James Harper's late strike lifted the Royals out of the relegation zone after Marcus Bent's first Latics strike had cancelled out Dave Kitson's first-half opener.
Wigan had a number of chances to have won the game themselves before Harper netted and in the first half saw referee Keith Stroud award them a penalty which he then downgraded to a free-kick.
Coppell admitted: "It was a massive goal for us and came at a stage in the game when if anyone was going to win it it was them. We were affected by their goal. In the first half we played well but when we scored we lost a bit of an edge.
"In the second half once again we couldn't go five minutes without conceding. They seemed to grow with the goal and on a couple of occasions we had to defend with our life's worth.
"Then to score at the end, we have had a few things go against us so it was nice to have that break coming our way.
"It was desperately important to win and there is no use hiding it. I said beforehand that it would be psychologically important and it's not how you win a game, just the fact that you have won it - and we have won it. Not in a convincing fashion but we have won it and we are out of the bottom three."
Wigan manager Chris Hutchings was convinced his side should have wrapped the game up well before Harper's goal with Bent allowing himself to be tackled by Michael Duberry in the box and substitute Julius Aghahowa seemingly impeded by goalkeeper Marcus Hahnemann in another attack.
The Nigerian might have gone down but opted to carry on in the hope of scoring but Hutchings was annoyed he had allowed himself to be caught up by a defender.
He said: "I don't know whether he stumbled or the 'keeper caught him but we still should have scored. We had two opportunities that we should have made better use of and if we had done that we would have won the game.
"It was not given, he stayed on his feet so we can't bleat about it now."
Coppell added: "He wasn't completely wiped out was he? He didn't have full control of the ball. The delay did us a favour because we had people chasing back. The player wanted to stay on his feet to be fair."
On the penalty that was taken away Hutchings added: "That was a big decision and if he (the referee) has got it right then all credit to him."
PA Sport