The Glaswegian led Burnley into the top flight for the first time in 33 years last summer, but has reaffirmed his desire to become Bolton's new boss following Gary Megson's sacking last week.
Bolton are currently trying to thrash out a compensation deal with Burnley for Coyle and Allardyce - who enjoyed a successful eight-year stint as Wanderers manager - thinks the Clarets should have pulled out all the stops to try and hold onto their man.
Asked if he thought Coyle would be successful at the Reebok Stadium, Allardyce said: "Yes, I'm sure he will. I think it's a big loss for Burnley.
"They should have broken the bank to keep him because he has shown to be single-handedly, the key, most important person at Burnley for many, many years.
"They should have gone a lot farther to try and keep him.
"Bolton have got themselves a very good young manager if that gets sorted out over the next few days."
Source: Team Talk
Source: Team Talk