Celtic have been the dominant force in the Scottish Premiership for years, but the champions were humbled 5-0 by Paris Saint-Germain in the Champions League recently.
Bellamy, who spent five months at Celtic in a five-month loan spell in 2005, insisted that no one in English football is impressed with Brendan Rodgers’ success.
“I found out during my time in Scotland, it doesn’t matter what you do up there – no one cares,” said Bellamy.
“I had more offers in January, before I went to Celtic, than I did when I finished my time up there the following summer.
“That’s because once you went up to Scotland nobody in England gave a damn what you did up there.
“If you do well up there, it’s a case of ‘so you should’.
“I just didn’t feel it mattered to anyone down south.”
As Celtic prepare for the short trip to Ibrox to take on Rangers on Saturday (12pm), the matter was raised with the Parkhead manager.
Rodgers, unsurprisingly, totally dismissed Bellamy’s jibe.
“I am not here to boost a CV – I am here because of Celtic,” he said.
“My life has always been about developing players – if we can win trophies along the way, then great.
“I respect Craig, he is very passionate about his life, very passionate about his football.
“Seeing some of the comments, I am not sure it is meant in that way but if it is, then OK.
“I am not here to worry about my next job, my only worry is Celtic and that is what I am paid to do.
“You can’t say there’s no interest. There’s always interest, wherever you go in the world.
“I’ve been in enough changing rooms in the English Premier League where the boys are glued to it if there’s a Celtic-Rangers game on.
“I’ve been at Chelsea, Swansea and Liverpool. They think ‘bloody hell’ and ask what type of game it is to play in.
“If there is a Celtic-Rangers game on, people throughout the world will want to hear about it.
“It is a worldwide game. It is a box-office game, no question.”