Coyle left Latics "by mutual agreement" after a run of three successive home defeats in nine days and Whelan was present for the most recent loss, Sunday's 3-1 drubbing by Derby, where he later expressed his disappointment to the manager over the performance and his team selection.
Judging by the crowd's reaction, Whelan's concerns were shared by the home faithful and, once Coyle offered to end his six-month stay at the DW Stadium, his chairman duly obliged.
Whelan had spoken of his happiness with Coyle's start to life as Roberto Martinez's successor on a trip to Barbados last week, only to change his tune once he witnessed Sunday's performance and gauged supporters' feelings.
Speaking to Sky Sports News, Whelan said: "Things happen fairly quickly in football. We have lost three home games in a row and, actually, I didn't sack Owen.
"I had a meeting with him after the match and I told him I was disappointed in his performance, the performance of the team and I was disappointed in the team selection.
"Owen said did I want him to resign? I said 'yes'. If you'll resign, obviously we've got to pay compensation, etc. But I accepted it and he's resigned."
Derby went 3-0 up inside 29 minutes in front of the watching Whelan and he would have noticed not just the jeers which greeted such a scoreline, but also Coyle's post-match comments where he suggested certain supporters' expectations were too lofty.
However, Whelan has aspirations of returning to the Barclays Premier League where Wigan spent eight years prior to last term's relegation and he insists Coyle's departure was the best thing to help achieve that goal.
He added: "I was so disappointed with our performance yesterday and the two recent home performances. The crowd were getting on to him yesterday and they did it in the last two home games. It's not something I like to do when I lose a manager. You've got to a appoint new manager and it's never, never an easy task."
It is one which he must undertake now, though, and Whelan stressed the need to appoint a new boss as soon as possible.
Latics, currently 14th in the Sky Bet Championship, will be managed by first-team coach and former boss Graham Barrow along with assistant manager Sandy Stewart at Leeds on Wednesday night.
They can still qualify for the last 32 of the Europa League and are just six points off the play-off berths in the Championship, making them a very attractive proposition for somebody.
"I've got a completely open mind," Whelan said when asked what he was looking for in any potential suitors.
"I think that's the right way. I've got to have an open mind and see if I can figure out who is going to be the right man.
"It's never easy. Appointing a manager is very, very difficult. You can be very lucky and get the great guy, the right man like I got with Roberto. You can be unlucky and get someone who doesn't get on with you, doesn't get on with the team and doesn't get on with the fans and that is actually what happened with Owen."
Coyle earlier expressed his disappointment at leaving, saying: ''It is with great sadness that we have made this decision and I would like to thank all my football staff and the staff at the club, who have been very supportive of me in my time here.
''I am confident that with this set of players, the team can keep moving in the right direction.''