The Trotters are currently second bottom of the table on just nine points, and face Alex McLeish's Aston Villa on Saturday, with Coyle suggesting both managers have a strong enough chin to take any negative comments that come their way.
"We all know the nature of the game we are involved in and I've said before, so long as people are not personal in terms of their criticism, then so be it," Coyle said.
"We have all been in the game long enough and are big enough and ugly enough to accept what goes on.
"Alex [McLeish] knew the challenges he was going to face and he also knows, as I do, that when you are winning games everything is rosy in the garden."The Villa boss has fared better than his compatriot so far this season, and after switching from rivals Birmingham City for Villa Park, he has led the club to ninth place in the league.
During the west Midlands side's recent 1-0 loss to Manchester United, McLeish faced a backlash from his the club's supporters, however, Coyle had high praise for the former Rangers manager.
"He is a friend of mine; he signed me from Dundee United and I played for him [at Motherwell] and loved my time under him," Coyle said.
"He is a terrific manager and, more than that, he is an outstanding man, somebody I have got a lot of time for.
"He is very passionate and loves his football. He has done a terrific job wherever he has been.
"Of course there was going to be a furor about moving from Birmingham to Aston Villa, but he took that on the chin and accepted it for what it was, because we understand that in football, that everybody has their opinion.
"It is something as managers that we learn to deal with. I certainly try to with a smile on my face and Alex is also very much in that mold."