Wanderers are rooted in bottom three following back-to-back defeats against Norwich and Wigan which has led to certain sections of the Trotters faithful calling in to question Coyle's tactics.
Bolton are only a point off safety but with daunting trips to Manchester City and Chelsea up next, Wanderers could find themselves in serious trouble if they lose both and other results go against them.
However Coyle is staying positive and believes that Bolton will still be a Premier League club at the end of the season.
"You will always get dissenting voices, but in the main we have a fantastic core of support who are invaluable to us," Coyle told the BEN. "I think they can see what we are trying to put in place in the long term. But I have to address what we are doing in the short term.
"I want my players to share the passion and enthusiasm I have for Bolton Wanderers. And if we do that, come the end of the season, I believe we will be sitting with a smile on our faces.
"We will be in a position where the club has never been for many years."