A missile from the main stand at Tynecastle hit the Hibs manager in the face near the end of the goalless draw. Lennon had been gesticulating to the Hearts fans after the Gorgie side had had a goal disallowed late on.
Lennon went down clutching his face.
“I’m all right, I got a couple of quid,” Lennon said afterwards, trying to make light of the situation, before adding: “It’s no laughing matter.
“I hope someone deals with it and I hope to meet the guy face-to-face.”
On a night when incidents off the pitch overshadowed the football, Hearts goalkeeper Zdenek Zlamal appeared to be struck by a supporter behind his goal.
Asked about this on BT Sport, Lennon said: “It’s not on, it’s disgraceful. People are trying to do their job. I don’t understand the mentality.
“They should be punished and they should be banned.”
Hearts manager Craig Levein said: “People who do this don’t deserve to be watching football.”