Having guided Burnley into the top flight last summer for the first time in 33 years, Coyle went from hero to zero in the eyes of many of the club's supporters when he left for the Reebok.
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"We were always up against it, but what we did was more than remarkable and we took the fans along with it. We asked the fans for that passion and it is a remarkable football club. Whatever happens, that will never leave me.
"I'll always have a special place for Burnley football club and if fans want to come and vent their anger and frustration at me, then so be it."
Coyle, 43, remains confident that in time, the memory of his achievements at Burnley will outlast those of his departure.
"It's happened and we have to get on with it. But what I do know is the job we did and I say we, because we did it collectively at that football club was remarkable over the course of two years.
"As time goes by I think everybody will look back and realise that it was such an important part of the history at the football club."
Coyle denied he was placed on "garden leave" after making his desire to join Bolton known to the board at Turf Moor, and insisted he did everything in his power to ensure Burnley received a fair compensation package.
Manchester City midfielder Vladimir Weiss became Coyle's first signing for the club on Monday after joining on loan until the end of the season.
The Slovakia winger is looking for first-team football ahead of his country's World Cup campaign having been on the fringes at City, and the 20-year-old is in line to make his debut against Burnley.
Coyle is also hopeful of tying up a deal for 24-year-old American midfielder Stuart Holden, who has been on trial with Wanderers after leaving Major League Soccer side the Houston Dynamo but is currently nursing a thigh injury.