Brazil star Neymar scored a hat-trick as the visitors slumped to their heaviest defeat in Europe since they lost 5-0 away to Artmedia in a Champions League qualifier in 2005 and the result confirmed the Hoops' status as the bottom side in Group H with three points from six games.
Barca defender Gerard Pique opened the scoring from close range in the seventh minute before Pedro Rodriguez and Neymar added a second and third before the interval.
Neymar scored his second two minutes after the break before grabbing his hat-trick and substitute Cristian Tello got in on the act in the 71st minute when his drive was heavily deflected past Fraser Forster by Parkhead defender Virgil van Dijk for number six before Georgios Samaras grabbed a late consolation for the Scottish champions.
An "angry and disappointed" Parkhead boss said: "Barcelona were fantastic as we expected them to be but we were very poor.
"I wouldn't say some players gave up but it certainly looked that way at times.
"I would never accuse a player of doing that but a lot of half-hearted performances and as a manager that was the most disappointing aspect of the whole game.
"There was no bravery on the ball tonight, we started off nervously and it looked like our heads went down at 2-0.
"We were weak and that has not been like us, that is something I have to address going forward.
"It is a sore one and I am hurting a little bit as are the players.
"It was unacceptable from some of the players, nowhere near the performances against Barcelona recently so that was very disappointing, obviously.
"There were only two or three players who showed anything, Virgil van Dijk, Adam Matthews and Mikael Lustig and I excuse the goalkeeper (Fraser Forster) but the rest of the team were very very poor, well below the standards set in the last few years.
"It was really tough to take. We were playing a great side but we were better than that.
"We will have to analyse it and look at the character which was there tonight."
Lennon explained what had looked like some bold changes to his starting eleven.
Top scorer Kris Commons, with seven goals in his last four games, and stalwart Charlie Mulgrew, and striker Anthony Stokes, were dropped to the bench as defender Matthews returned after a 10-game absence following shoulder surgery.
Lennon said: "Charlie wasn't 100 per cent fit, he had a groin problem and didn't train so we felt he wasn't ready to start and in terms of Kris, we just wanted pace down the flanks with Teemu Pukki up top to stop the full-backs getting forward but we didn't achieve that.
"The players didn't do their jobs they were assigned to do."
On Neymar's scintillating performance, the Northern Irishman said: "I was impressed with him at Celtic Park, he is a talent and has a great future in the game."
Barca boss Gerardo Martino was delighted with his side's emphatic victory, describing it as the "most complete match of the season" and is confident there is more to come from his players in the weeks and months ahead.
"I am very happy with the quality of the performance tonight," he said.
"Our play is improving all the time and I expect better by the end of the year.
"There is always room for improvement and that is what we are striving for.
"We have a bunch of players playing brilliant football and have been doing so for a long time.
"Hopefully this is the breakthrough moment this season."