The image, which is being investigated by police, showed an unidentified man standing in front of a television, holding what appears to be a kitchen knife up to the neck of Mr Lennon, who was on the screen.
It was posted on a Celtic supporters' Facebook page shortly after the team lost against Barcelona in the Champions League match on Wednesday night.
Mr Lennon said: "It is not upsetting for me, but it is upsetting for my family more than anything else.
"It doesn't affect me all that much, but what is concerning is the mindset of some people.
"Whether it is innocent or they think it is funny, for me it is disturbing.
"You like to think those days have gone but obviously not."
The Celtic manager also spoke about the furore since club captain Scott Brown received a red card in the game on Wednesday night, after kicking Barcelona player Neymar during the second half.
He said the menacing knife image on Facebook had been "sort of laughed off, whereas Scott does something on the pitch and he is treated far more harshly than what other people are".
"You have to have a sense of perspective on this."
Mr Lennon said the incident reminded him of when he was threatened in the past, after receiving home-made parcel bombs at the club's Lennoxtown training complex in April 2011.
The manager's lawyer, Paul McBride, QC, and former MSP Trish Godman were also targeted with the rudimentary explosives.
Two men were later found guilty of conspiracy to assault, and were jailed for five years.