A bottle was thrown at Celtic forward Scott Sinclair from the stadium's East Stand, while Hibs also reported of another incident which involved one being chucked on to the field of play from the stand housing Celtic supporters.
It comes just days after Hearts goalkeeper Zdenek Zlamal was hit by a coin during last Wednesday's clash with Celtic, while earlier in the season, Lennon and Zlamal were both struck by objects during an Edinburgh derby on Hallowe'en last year at Tynecastle.
Heckingbottom said: "No-one wants to see things like that. It's been a bit topical recently. Whoever has thrown it, we need to find them. It seems to be happening a little bit too often right now. We need to try and stop it."
Lennon said: "It's just got to stop. It's not just confined to one individual ground, it's all over. The players and officials and management staff should be protected - it's their environment that they entertain in. It's not on."
Celtic won the match 2-0 and progressed to the semi-finals of the competitions after goals from James Forrest and Scott Brown, inflicting a first Hibs defeat on Heckingbottom.