The former Bolton boss' offer to resign was accepted by Whelan following the 3-1 loss to Derby at the start of December, after which the Latics chairman had expressed his dismay at Coyle's tactics and selection.
Coyle has kept his counsel since his acrimonious split but, speaking on Friday night, admits there is no lingering resentment towards Whelan or the club now managed by Uwe Rosler.
"I'm not bitter and twisted, there are a lot of good people at the football club and I wish them well," he said on 5 live Sport.
"They've got a lot of good players, they're great lads to work with and I thoroughly enjoyed my time there.
"The bottom line was myself and the chairman never saw eye-to-eye on a few things. Now, I could go into detail on that but I'm not prepared to do that. It's happened, I move on and I wish Wigan Athletic nothing but the very best."
Whelan had made a startling U-turn on his belief that Coyle was the most suitable man for the job after waxing lyrical about the start he had made at the DW Stadium just a week before his departure.
However, having returned to the country and been present for the defeat to the Rams, Whelan and Coyle clearly had different opinions when it came to Wigan's future.
The latter added: "Dave Whelan's a passionate man, it's his football club. He runs the club and he's got his own opinions on things.
"He's got his own favourite players and Dave Whelan's favourite players may not be my favourite players. If everybody's not singing from the same hymn sheet there's only going to be one ending from it.
"When we left, I shook his hand and we wish them well. I truly hope Wigan get promoted. Uwe Rosler's come in to a great set of players, he's worked hard at Brentford to earn the right so good luck to him. They're a good club with great people and I wish them well."