The Portuguese manager infuriated the Aberdeen manager with comments about the Dons’ cycle coming to an end with the expected departures of Niall McGinn and Ryan Jack.
It provoked a rebuke from McInnes, who shot back stating that the Rangers boss should be “embarrassed” finishing third, behind his Aberdeen side put together on a lesser budget.
Speaking on BT Sport ahead of the Premiership play-off match between Dundee United and Falkirk on Tuesday night, Lennon said McInnes had every right to criticise Rangers.
“I think he has been average to say the least,” Lennon said. “He talks great in front of the cameras, looks great. We all talk a great game about tactics and formations and this that and the other, it’s a results driven business. I don’t think there has been any improvement since (Mark) Warburton left.
“I agree with Derek. I thought Derek was quite spikey in his press conference but he had every right to be. I think Derek has done a fantastic job and he’s right Rangers should finish above Aberdeen and he should not be talking about what Aberdeen are doing, about cycles. Derek McInnes just builds on what he has already built and they’ve been so consistent over the past few seasons.
Chris Sutton also backed the Aberdeen manager.
“Pedro’s got under his skin,” he acknowledged. “Derek McInnes is quite right. Pedro Caixinha should concentrate on his own club and finishing above Celtic, Aberdeen shouldn’t be the benchmark for Rangers.”
Lennon was also critical of the way Caixinha spoke openly about the club’s interest in Aberdeen captain Ryan Jack who is out of contract at the end of the season.
“He shouldn’t talk about players who are still at a club,” he said. “A lot of clubs like ourselves would be interested in Ryan Jack but you don’t talk about it publicly and I think that irked Derek as well and he has every right to have a go back.”