The Israel international, speaking to a newspaper in his homeland earlier in the week, claimed McCulloch was a dirty player who deliberately injured him during an Old Firm encounter at Celtic Park in 2011, with the 25-year-old consequently spending several months on the sidelines.
It was also reported that Kayal, who joined the Parkhead club in 2010, claimed there is a "lack of technique" in the Scottish game.
However, the Hoops boss, ahead of Saturday's trip to Dundee United in the Scottish Premiership, put the controversy down to "mischief-making" within the Scottish media.
"In terms of his quotes, I am not entirely convinced that they are factually correct. Having spoken to him and seen parts of the interview, I do believe there has been a bit of mischief-making on this side of the continent," he said.
"However, he did it without my consent so I am obviously not pleased with that and he knows that and he will be dealt with.
"I think those quotes about league, certainly, were entirely misconstrued and the context of the interview in essence, there has been bits and pieces taken out of it to suit a certain spin, if you want to put it that way.
"I know it is an easy excuse, but I think he has a valid argument in this.
"But the issue is that he did it without my consent or the club's consent, and we regard that as a misdemeanour and he will be dealt with."
While it appeared that Kayal was angling to leave the champions at the end of the season, Lennon insists he still has a part to play with the champions.
"I don't think he has been happy because he has not been playing, but I think he is happy being at Celtic and it is up to him to show what he can do," the Northern Irishman said.
"He has found it difficult to get back into the team, such has been the form of Scott Brown, Stefan Johansen and Charlie Mulgrew, but he will get an opportunity between now and the end of the season.
"I know there is still a very good player in there, but it is difficult for him to replicate the form of his first 18 months here, due to horrendous injuries."
The former Celtic skipper has also had to deal with Leigh Griffiths, who was issued with a notice of complaint by the Scottish Football Association this week for "singing in public about Hearts in administration".
The 23-year-old, who joined the Parkhead club from Wolves in January after having spent two spells on loan at boyhood heroes Hibs, was filmed before last Sunday's Edinburgh derby at Tynecastle, which he attended, chanting about the Gorgie club's plight and was cited on rule 86, which relates to "not acting in the best interests of association football".
A principal hearing date of April 24 has been set for the case, which Celtic will defend, although they have fined the player and apologised to Hearts.
"I wasn't over enamoured with it," Lennon said.
"We have dealt with it as a club and we have told him there is a certain code of conduct he has to adhere to when he is here at Celtic.
"He didn't use bad language or act in an aggressive manner, but it hasn't pleased me.
"I can understand why the SFA have become involved - they have guidelines - and I can understand people who probably rung the SFA to complain about it as well.
"There will be people on the Hearts side who will think it is insulting and derogatory. From my point of view, he probably shouldn't have put himself in that position in the first place but, from the other point of view, is it the worst thing in the world that he has done? No.
"I don't mind him supporting Hibs, Hearts or Tottenham Hotspur, whoever, but in public places he has to behave accordingly at times.
"He is a Celtic player now and his whole focus should be on Celtic."
On a more upbeat note, Lennon praised his 17-year-old midfielder Liam Henderson, who picked up his Scottish Premiership young player of the month award for March at the club's Lennoxtown training complex.
The Hoops boss said: "He has been absolutely excellent since he came in. The challenge for him is to stay there - it is not just a question of coming in for two or three games and fading away. But I don't think it is that is his type - his attitude is fantastic."
Henderson said: "Making my first start and scoring against Partick Thistle, it has been one of the best months of my life so far.
"It couldn't have gone any better and it has really helped my confidence so I am delighted."