Coyle has bounced back from dismal lows several times before - while in charge of Burnley and St Johnstone.
And he said: "It was a terrible day at Wembley and we'll all be hurting until the day we die.
"But it's happened and I can't affect that now. You need to take that hurt and disappointment and motivate yourself to move on.
"I've sat with a St Johnstone team, after playing 50 games, waiting for a result in the dressing room to see if we were league champions and it didn't happen.
"We had to pick them up and we did.
"Then at Burnley we reached the Carling Cup semi-final and lost in extra time. We went again and got promoted to the Premier League.
"We must now show our mental response against a great team in Arsenal."