O'Neill, 61, was shown the door at the Stadium of Light by American owner Ellis Short following the club's 1-0 defeat to league leaders Manchester United.
That result meant the Black Cats have now gone eight games without a win and leaves them just a point clear of the relegation zone, with both Wigan and O'Neill's former club Aston Villa having a game in hand.
Ex-Crystal Palace and Reading boss Coppell does not believe it was the loss to United that cost O'Neill his job and reckons the make-up of ownership in the Premier League has an impact on the life span of a top-flight manager.
"For me I can only think there was a personal confrontation after the game as Martin, in his interviews after the game, looked calm, collected and inspired for the challenge ahead," Coppell told BBC Radio Five Live's Sportsweek.
"You can only presume there was some dialogue after the game, we are in the realms I'm afraid of spoilt-brat reactions because it is their toy.
"They don't understand the history and heritage of British football - there are so many foreign owners, I have nothing against that, but there is a way of doing things in English football that has now gone out of the window.
"For me it is some sort of personal confrontation that has happened after the game and perhaps it was obvious that they are going in different directions."
The decision to relieve O'Neill of his duties with just seven games remaining has also been questioned by Coppell.
"We have just come on the back of an international break," he said. "If you were going to make a change constructively you would have made it then. Now you can't do that kind of thing and whoever comes in has got an almost-impossible task."
Former England manager Steve McClaren has been installed as the early favourite to replace O'Neill, with an announcement expected well in advance of Sunderland's trip to Chelsea next Sunday.