An Anthony Stokes hat-trick ensured the Hoops of a safe passage to the competition's next round with a 3-0 win but Lennon was particularly unhappy with a challenge by Peterhead midfielder Jamie Redman on Joe Ledley which resulted in the Wales international being withdrawn after suffering a facial injury.
He said: "I wasn't happy with the challenge on Ledley but the referee deemed that to be accidental. There were a few meaty challenges going around but you expect that when you come away from home in the cup."
He added: "You are always worried as you can get injuries at any time. We have obviously lost Beram Kayal this week and he could be out for a concerted period of time. You want to restrict the injuries to a minimum if you can.
"I think we were just a bit quicker to the ball at times. I don't think there was any real malice in the challenges but Joe was definitely caught with a swinging elbow."
Peterhead manager Jim McInally defended his side's approach to the match.
He said: "I did think the players showed a lot of aggression and there was a lot of angry Celtic players at times. The first half hour was probably our best spell in the game and it was disappointing that we didn't have more shots on goal or crosses into the box. We worked that hard to get the ball back that we were sometimes tired by the time we eventually got it."
And the Peterhead boss said he felt Redman had made an honest attempt to head the ball when challenging with Ledley.
He added: "He has a cut eye so I don't think it was anything other than two guys clashing heads. I haven't seen it again but if he has elbowed him then how has he got a caught eye himself? That was why the ref made him come off for treatment. I might be wrong but to me it was just a clash of heads.
"If he (Lennon) is annoyed then he is annoyed, but we can't just stand back and let them play. We had to try and get in about them and to be fair to our players they did that."