Celtic looked off the pace in the early stages of Saturday's Scottish Premiership encounter at Kilmarnock before hitting their stride with a goal from Kris Commons and two in as many minutes from Georgios Samaras.
Killie fought back to make it 3-2 at half-time, but Samaras completed his hat-trick with three minutes left before Amido Balde made sure of the points in added time.
Lennon was also critical of the way his side let Killie back into the game, and he knows they must cut of the mistakes if they are to repeat last season's famous win over the Spanish giants.
"I thought we were sloppy at times and a wee bit pedestrian at the start," admitted Lennon after the 5-2 win at Rugby Park. "I don't know if it was the weather or the pitch, we just looked like we were out for an easy-ish type of game.
"I didn't think we started the game well at all. After the first goal the reaction was superb and I thought the second and third goals were quality.
"Then we got a bit lackadaisical at the back. Virgil van Dijk gave a free-kick away when Michael Gardyne was not going anywhere and we got done on a give and go.
"Obviously I wasn't best pleased at half-time but I thought the second-half performance was superb. I thought we dominated the game and limited Kilmarnock to very little and we looked a threat going forward.
"But I don't think we will (start slowly against Barcelona). I think the temperature will be cooler, we will be under the lights and we are playing Barcelona.
"They are notoriously fast starters, in the recent game against Sociedad they were three up in 15 minutes so we have to be very wary of that.
"But psychologically, the win today gives the players great confidence going into the game."
Lennon will welcome winger James Forrest back from a virus and midfielder Beram Kayal has recovered from a groin strain, Adam Matthews had to go off against Kilmarnock with a possible virus.
"Injury-wise we are okay," Lennon added. "Adam felt a bit ill. Maybe there is a virus going about so we have to keep an eye on that but with Kayal and Forrest joining the squad on Sunday, we are looking a wee bit more vibrant again."