The football boss added a wreath to the hundreds of bouquets placed at the scene where nine people are now known to have died.
He said there was an "eerie atmosphere" at the site where a helicopter plunged into the roof of the packed bar.
Mr Lennon said: "It's an unforeseen tragedy that's affected the whole city, and the city is united in grief at the minute.
"There's an eerie atmosphere around the place at the minute, which you can understand.
"I was out myself on Friday night with some friends when I heard, so it puts a lot of things in perspective."
The Celtic boss laid a wreath on behalf of his club before taking a look at the tributes already lining Stockwell Street.
He placed the green and white bouquet among other floral tributes, candles and cards that had been laid by visitors to the scene throughout the day.
Mr Lennon then took time to walk along the floral display, reading cards and tribute messages left by mourners and well wishers in rows along the pavement.
A card on the Celtic wreath read: "They never die who live in the hearts of those they leave behind.
"In the thoughts and prayers of everyone at Celtic FC."
Paisley victim Gary Arthur, 48, is the father of student Chloe Arthur, a Celtic and Scottish women's footballer.
Mr Lennon said he felt it was important to pay tribute at the scene as the club has an "indirect" connection with the disaster.
He added: "Our own club has been affected indirectly with a young girl who plays with the ladies' team losing her father, so I just wanted to come down on behalf of the club and pay respects to all the people involved.
"It's very difficult for me to find the right words at this time for (the victims and families) but, on behalf of myself and the club and the Celtic support, we're all thinking of you and you're very much in our thoughts and prayers at this time.
"This has been a terrible accident that will affect so many people, not just those in Glasgow."
Earlier in the day PFA Scotland chief executive Fraser Wishart visited the scene to lay flowers.
A group of young female footballers wearing Strathclyde University sweatshirts also laid a floral tribute at the site, shortly before Mr Lennon's visit.
Around 450 floral tributes have been placed across the road from the Clutha Vaults, outside the Holiday Inn Hotel. Some well wishers knelt to say prayers.
Two police officers standing guard escorted those seeking to show their respect for the people who did not survive Friday night's disaster.
Along with floral tributes and candles, well wishers brought boxes of biscuits and chocolates to give to emergency services working at the scene as tokens of gratitude for their hard work.