Allardyce took over at Newcastle a month later on a three-year contract but was in charge for only 24 matches before leaving the club "by mutual agreement".
He had to wait 11 months before resuming his career with Blackburn, who face Mark Hughes's Fulham this weekend with the London club just one one of five teams still unbeaten in the Premier League.
And with Hughes arriving at Craven Cottage for the start of the season having been sacked by Manchester City after an 18-month stint, Allardyce feels the former Welsh manager, as well as himself, has not been given time to perform with certain clubs.
"His Manchester City reign obviously was not long enough. A little bit like me at Newcastle, but I didn't last quite as long as Sparky though," Allardyce added.
"He was given the chance and unfortunately at that stage of his career they decided to have a change. You look back on it and he'll be very disappointed because they only lost two games.
"There's a perception that other people can do better than you, but often the reality is not the case. He decided that Fulham was the place for him, he's taken over what he's described in his own words as a very good team and he's started where they left off last season."
Sam has made his mark in the Premier League, which is the strongest league in world football
Hughes, meanwhile, believes Allardyce would be a strong candidate to be the next England boss, with Fabio Capello set to step down in two years.
Allardyce was pipped to the England post after the 2006 World Cup by Steve McLaren but Hughes said: "Sam's record in the Premier League stands comparison with any British, English or foreign manager at the level of the clubs he's been at.
"He's a successful Premier League manager and the view at this time is that England need an English manager. I also hold that view because it's important that a country is led by someone of the same nationality.
"Sam has made his mark in the Premier League, which is the strongest league in world football. If you can get positive results in this league you're a good manager.
"Whether the way Sam sets up his team lends itself to international management is a debate for another day. But certainly his record in terms of games won makes him a strong candidate."
Fulham's visit to Ewood Park on Saturday sees Hughes returning to the club where he spent three seasons as a player and four years as manager.
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