A goal from Chung-Yong Lee gave Bolton victory and Coyle said: "Perhaps they should call me Moses, as I led them out of the wilderness."
The comment was made without malice as the Glasgow-born boss is still perplexed at how much bitterness there remains at his departure after he led the club into the top flight.
Coyle, who made a point of applauding the Burnley supporters at the end of the game, said: "Until my dying day, I wish the club nothing but the best.
"This was more emotional than any other game I have been involved in. I left a unique club and know the passion that surrounds the place.
"Burnley are special and I will always hold them in the highest esteem. But they have the smallest budget in the league. They did not want to move at the same pace as me.
"The only person who knows the full story is me and I maintain I conducted myself properly."
Lee made the breakthrough in the 34th minute with his fifth goal of the season after a clever ball from Kevin Davies.
That goal was enough to take Bolton out of the relegation zone and put Burnley in it.
Coyle said: "There is a stigma in being in the bottom three and it is fantastic to be out of there.
"We gave two good performances against Arsenal without any reward, so it is very pleasing to get this win. The players just need to believe in themselves a bit more.
"I do believe ourselves and Burnley will stay up. Burnley played with courage and heart, which I knew they would."
Burnley manager Brian Laws was left cursing his luck as Chris McCann (knee) and Graham Alexander (calf) both came off injured in the opening stages. Then Michael Duff suffered a shoulder problem.
Laws said: "Our game plan went out of the window in the first 15 minutes and we had to re-organise then and at half-time.
"While we need to defend better, the players are suffering and we could do with some new faces by the end of week."