The ex-Celtic striker believes his old team-mate may be on a hiding to nothing with some fans because they never wanted him in the first place.
He feels this was partially down to links with some of the most famous managerial names in world football, stories Sutton has called "b******t".
He wrote: "I can’t believe the grumblings after just two competitive games – and wins – as Celtic sailed through their toughest ever first-round Champions League qualifier against Sarajevo with a 5-2 aggregate win.
"The negativity from a large section of the support who didn’t want Lennon was probably inevitable but it will only have an adverse effect on the team and the club as a whole.
"There’s a lot of work to be done and everyone, including Neil Lennon, realises that. But to be criticsed after winning 5-2 on aggregate? I just don’t get it.
"And I’ve yet to hear a realistic alternative. All the stuff about Rafa Benitez and Jose Mourinho was the biggest load of b****** ever.
Andre Villas-Boas was another name to excite fans but he hasn’t made the best start at Marseille after pre-season defeats at Accrington Stanley and a 4-0 loss to Rangers - and that’s for a reported £6 million a year."