Rovers tackle Everton in Saturday's Premier League season opener at Ewood Park and while some clubs chop and change their manager regularly, Everton have not.
David Moyes is now in his eighth year as Everton boss and Allardyce believes the Merseysiders are benefitting from standing by their man through thick and thin.
In a week that saw Martin O'Neill resign as Aston Villa boss, the ex-Newcastle and Bolton manager knows that success must be built from solid foundations.
Bristol City also have a new man at the helm following Steve Coppell's shock resignation and Allardyce has reiterated that football managers are under enormous pressure to deliver.
"It is a rarity now and Everton are extremely fortunate to have kept David where he is because of the work he has done and how hard he has worked to turn the club around from what was a difficult position when he took over," said Allardyce.
"David and the club fit very nicely and they are reaping the benefits of stability and the backing of a manager and good working relationships.
"It is something that lots more clubs in the Premier League, and certainly the Football League, should take notice of because without that stability you are not going to bring any sort of success to a club.
"It tells you about the enormous pressure of being a manager. We make the decisions we make because people don't see it in the same light we see it.
"In Steve's case, it is the second time it has occurred where he is not comfortable in the surroundings - it happened at Manchester City a few years ago.
"Rather than it lingering on and damaging the club or him, they have decided to part company. Martin has decided it is not longer viable for him to carry on at Aston Villa."