Fenlon brushed off the claim after Saturday's Scottish Premiership game but striker Rowan Vine hit back at Lennon on Twitter after being singled out for committing what the Celtic boss described as a "rugby-esque" challenge.
Vine refuted the accusation and added he "might get me mate Alan Shearer to send him another size 9 Umbro Speciali in the dish if he don't pipe down..." - referencing an incident between Lennon and Shearer whey they were players.
The 31-year-old later apologised for any offence when questioned by Lennon on Twitter and Fenlon has spoken to the Englishman about the issue.
"I've dealt with it in-house and we have moved on from it," Fenlon said.
"We want to do our talking on the football pitch and that's it. That's as far as we want to do and as far as we want the players to do.
"That's what we get paid for, to do our work on the pitch and leave the talking to other people."
Defender Michael Nelson also responded to the criticism on his Twitter account and posted a photograph of himself with a black eye that could yet prove more serious than bruising.
The centre-back looks set to miss Saturday's visit of Aberdeen but Hibs do not yet know the full extent of the injury.
"He is in the hospital now so we are waiting to see what the damage is and how long he will be out," Fenlon said.
"He has got a lot of bad bruising around the eye."
Fellow defender Ryan McGivern went off injured against Celtic but Fenlon is only missing Tim Clancy and Alan Maybury from his back four along with Nelson.
"Ryan is fine, he has trained all week," the Irishman said. "James McPake is back and Jordon Forster has trained all week.
"We seem to get one back and lose one in that position but we have good cover now."
Hibs will move into fourth place if they win on Saturday and Fenlon is looking for the same commitment from his side against the Dons.
"It's a big game for us, we have the chance to jump a team ahead of us," he said. "But they are a good side and they have had a good start to the season.
"We have to make sure what we brought to the table last Saturday is the same this week."