The Pittodrie striker received a straight red card for his challenge on the Norwegian and lost an appeal on Tuesday.
On his official Twitter account Cormack said: "Sam will take his ban, but the compliance officer has a duty to review Ajer feigning injury with his triple salvo (sic) and miraculous recovery after Sam gets the red."
He also called for Leigh Griffiths to be punished over a challenge on Lewis Ferguson but Lennon, speaking to BBC Radio Scotland before the Ladbrokes Premiership clash with St Mirren in Paisley, said: "It's absolutely embarrassing.
"I'm not having that at all. Kris Ajer is the victim in this and was on the end of a very heavy challenge.
"There was no feigning injury, there was no play-acting. Kris is a model professional and I am not having someone from the Aberdeen board, or anyone else, talking about my players like that.
"First of all, it isn't true - it's a lie. Second of all, these things should be kept in-house.
"We have been very balanced on the whole issue and have tried to play it down. But when you see comments like that coming out from the Aberdeen chairman, we are not tolerating it as a club - and I'm not as a manager.
"Every team in the country would want Kris Ajer - he's a model professional on and off the pitch.
"It's very naive from Mr Cormack. I'm hugely disappointed. It's an attack on my player and he has done nothing wrong.
"The comments are absolutely disgraceful."