Lennon had earlier questioned comments made by Vine in the wake of the Scottish Premiership draw between the teams on Saturday.
Vine had responded to Lennon's claim that he made a "rugby-esque" tackle on Darnell Fisher by writing on Twitter that he might get "Alan Shearer to send him another size 9 Umbro Speciali in the dish".
Lennon tweeted Vine to say: "Did I read that right" but he was in no mood to discuss the issue as he met the media ahead of his side's home clash with Ajax on Tuesday.
Lennon said: "I'm not here to talk about Rowan Vine, I'm here to talk about the Champions League."
The controversy started when Lennon accused Hibs players of making "absolutely shocking" and "reckless" tackles in a game which saw two of them booked.
Vine later wrote on his Twitter account, referring to an incident where Shearer was accused of kicking Lennon in the face during a Leciester-Newcastle game in 1998: "Read Sir Neil Lennon's comments regarding tackles in y'days game and said my tackle was 'rugby-esque'..I mean I know he likes the snus....
"But has he been smoking something else..I hardly touched the boy and there were no 'reckless' tackles in the game..
"Might get me mate Alan Shearer to send him another size 9 Umbro Speciali in the dish if he don't pipe down..."
Vine later apologised when contacted by Lennon. He told the Celtic manager: "Was light hearted, just thought your comment was poor, thought it was a good physical game.. apologies obviously if you've taken offence.."
Hibs defender Michael Nelson also referred to Lennon's comments as he posted a picture of an eyesocket injury he suffered during the game and wrote "ManUp".
Nelson stated on Monday afternoon that his injury was "not great" and that the full extent would become clear on Thursday.