The Celtic boss was on a scouting mission at the match between Aberdeen and St Johnstone.
But he was verbally abused and had coins and drinks thrown at him while sitting in the Main Stand at Tynecastle.
Lennon left the match with around 20 minutes remaining and admits he was "disappointed" with the shocking events.
He said: "I thought we were past all this. I thought with a neutral game like a semi-final, it would be ok.
"I'm there doing my job because we're playing Aberdeen next week.
"I've been to 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.
"Somebody could have been hurt and I'm not over-exaggerating that. Somebody could have been hit in the eye with a coin. It's just not on.
"That's when you've got to say 'well, maybe you 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.'
"I wasn't really shaken up afterwards but I felt for my staff as well and they felt for me."