Wigan owner Whelan accepted Coyle's resignation on Monday, ending the Scot's five-and-a-half-month spell in charge at the DW Stadium.
The 77-year-old is now preparing himself for the search to find Coyle's replacement, which he admits will be a tricky process.
"I've got a completely open mind," Whelan told Sky Sports News. "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 [Martinez].
"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 took charge of 23 games during his reign as Wigan boss, guiding the Latics to seven wins and 10 defeats.