Supporters congregated at Parkhead where they blasted the team and called for the manager to leave.
It saw scuffles with police and objects being thrown.
Speaking to The Times about his exit from the club, Lennon believes the players should have been “lauded” not lambasted as he criticised a new breed of fan.
He reckons the pursuit of the tenth title in a row was an “unhealthy obsession".
“Speaking to the players the next day they were really disturbed and upset by that," Lennon said. “Literally upset by it.
"That was the first cup defeat in 35/36 games. It was the end of an unbelievable cycle of success and for them to be treated that way was bewildering. They should have been lauded for it rather than abused.
"They were getting pelted with missiles. It was very sad. There was a new breed of supporters that I had nothing in common with and who belie the values of the club. They are the ones that are giving the club a bad name.
He added: “I had nothing in common with those supporters and the way they treated Dermot and Peter as well, shocking.”
Lennon bemoaned the lack of enjoyment of the club's achievements as they fell short of winning ten in a row with a resurgent Rangers waltzing to a title won at a canter.
The Northern Irishman left the club in February with the club 18 points behind Steven Gerrard's men and John Kennedy took interim charge.
“I wouldn’t say I was hurt, I was more bewildered by it and the lack of time and the lack of faith that people showed in me,” he said.
"It’s basically fans I’m referring to more than anything else.
"I can walk away with 21 medals as a player and a manager, the first guy to do the treble as both a player and a manager. If that doesn’t mean a lot to other people, it means a lot to me.”