Rodgers chose to leave Celtic and replace Claude Puel at Leicester earlier this week, despite stating to TalkSPORT back in April that Celtic was his "dream job" and he was "so happy" at Celtic.
But after a disappointing summer in terms of transfers, Rodgers was also prevented from bringing in more talent in January and has had to settle with using the loan market.
The disagreement between him and the Celtic hierarchy is perhaps a reason behind his departure, and former England boss Allardyce believes he has made the right decision - even if it upsets the Celtic fanbase.
“Brendan has made the right decision for Brendan – there’s no such thing as loyalty in today’s game,” Allardyce said. "He stayed at Celtic because he has kept Celtic winning everything, but now he's coming back to the best league in the world.
“I don’t want to upset Scottish fans, but that’s a fact. It’s the best league in the world, the most-watched league in the world and it’s the league where you need and would always want to be. All the best coaches are here.
“His patience wore thin in terms of investment at Celtic. He loves the club but at the end of the day the frustration of not being able to build a better Celtic has got the better of him and he’s given the Premier League another go.”
A banner was held up during Celtic's last-gasp victory over Hearts on Wednesday night, which read: "You traded immortality for mediocrity. Never a Celt, always a fraud."
Neil Lennon has since been reinstated as Celtic manager on a temporary basis until the end of the season, and his chances of earning the role permanently got off to a flyer with the 2-1 win at Tynecastle.
Rodgers, meanwhile, will take charge of his first match as Leicester manager on Sunday when the Foxes travel to in-form Watford. The Telegraph claims he is earning a whopping £96,000 a week.
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