Lennon confirmed he had coins and cups of liquid thrown at him and suffered abuse as he sat in the directors' box surrounded by Aberdeen fans, who were watching their team beat St Johnstone 4-0.
Lennon, who was sitting next to Hearts assistant manager Billy Brown and Celtic coach Garry Parker, feared for the safety of himself and those around him before leaving shortly after the Dons netted a third goal in the 62nd minute.
Lennon, whose team host Aberdeen in the William Hill Scottish Cup fifth round on Saturday, said: "It was very disappointing, uncomfortable if you want to use the word.
"It was a great atmosphere and I don't want to take anything away from Aberdeen's day, it was a great day for them.
"I think it was drink-fuelled
About 30 minutes into the game a coin whistled past my head and actually hit a gentleman in front of me on his back and he's an Aberdeen fan
I think he was either a member of the board or maybe with the staff because he was sitting in the director's box.
"Thankfully he wasn't that hurt as he had a big padded coat on
It's just hit him on the back, he's obviously aware of it and he's given the coin to a female steward.
"At half-time we were thinking about leaving, but they said 'look, we've got you seats closer to the press box'
So again, you don't mind the abuse, you can take that because you get that up and down the country.
"Then, when the third goal went in, a drink, I don't know what it was or what it was in, flew over our heads and landed in the press box
It hit two journalists and splashed all over their computers.
"We decided then, we weren't forced to leave, it was said it was best to leave for our own safety, and the safety of people sitting around us as well."
Lennon, who did not feel the abuse was sectarian, had thought he would be safe.
He added: "I thought at a neutral game, a semi-final where I'm only doing my job because we're playing Aberdeen next week..
I've been at all the grounds, I was at Motherwell the week before watching Aberdeen and I've been all up and down the country, and I've never had to put up with that before.
"It makes me think twice about going to games if that's the type of thing that's going to happen
It could have been worse, somebody could have been hurt
I'm not over-exaggerating it, someone could have been hit in the eye with a coin
It's just not on.
"Eventually you've got to say 'right' and maybe need to look at something else in your life if you can't go to a game and enjoy it when you're out working."
The Celtic fans showed their support to Lennon with a special reception during the 18th minute of their team's 1-0 win over St Mirren.
Lennon, who wore the number 18 as a Celtic player, said: "Fantastic
I can't thank them enough for that.
"It's something we don't hear very often in games where we're so much in control, but I think the supporters felt it meant a lot to me personally."
The Scottish Professional Football League, which organises the security arrangements at League Cup semi-finals, apologised to Lennon.
Chief executive Neil Doncaster said: "Given this occurred at one of our games, we'd like to apologise to Neil Lennon for this utterly unacceptable behaviour.
"The SPFL is united in its total condemnation of this type of incident, which has no place in a football stadium nor society overall."
Aberdeen earlier appealed for information to identify the culprits of the "completely unacceptable" behaviour.
The incidents happened yards above where Lennon was attacked during a game in 2011 by a fan who was later jailed for eight months.
The 42-year-old has been the victim of a number of crimes during his time at Celtic, the most serious of which saw two men jailed for five years for sending him parcel bombs.
Source : PA
Source: PA