Former Hoops striker Andy Walker, now a pundit, claimed Celtic's Champions League campaign "ended with a whimper" as they lost 4-2 on aggregate to Braga in the third qualifying round.
Celtic's 2-1 win at home over the Portuguese side on Wednesday night was not enough to prevent them dropping in to the Europa League, where they were today paired with Dutch side Utrecht.
The former Bolton player also criticised Lennon's summer signings but Lennon, without naming Walker, has reacted angrily in an interview posted on the club's official website.
The Irishman said: "I am not surprised at the criticism that has come but I am surprised at the areas where it has come from.
"I picked up a tabloid today and it was ex-players who were wearing a Celtic shirt at a promotional event for Tennent's and getting paid good money for it and then going ahead and putting the boot into the team, the club, the board and myself.
"I can't have that and will not accept that. One particular player criticised my signing policy.
"I said I was trying to bring British and Irish players into the club which I have done - Joe Ledley, Charlie Mulgrew, Daryl Murphy and Gary Hooper.
"I did try to go after (Jimmy) Bullard, (David) James and (Sol) Campbell but I was unsuccessful with that.
"But all he could think about were the Israelis, South Koreans and Mexicans, who I think will enhance and improve the club anyway. So he is a bit economical with the truth there."
Lennon continued: "He said we went out of the competition with a whimper.
"That's his opinion - and he also said we didn't have a sustained amount of pressure and there was a lack of crosses against Braga, which was, again, a falsehood.
"We put 37 crosses in. We scored from two and had 65% possession. I am not big on stats, but I have to use these to back up what I said after the game."
Lennon also defended his captain, Scott Brown, saying: "He was prompting attack after attack, winning the ball back and covering the ground. I couldn't have asked any more of him."
Turning his attention to the upcoming Europa League play-off games against Utrecht, Lennon said: "Whenever a Dutch team comes they will always try and play football and technically they are very good.
"We are familiar with one or two of Utrecht's players but we will be doing our homework between now and the first leg.
"We want to put on a good performance against Utrecht and take a lead over there and hopefully get into the group stages and anything can happen after that.
"One of the reasons why the players come here is for the Europeans nights and to sample the atmosphere, to play European football, and there is a lot to look forward to this season."