Celtic led by three goals after 27 minutes before Kilmarnock pulled two back ahead of the break.
"I thought we were sloppy at times and a wee bit pedestrian at the start," said Lennon.
"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."
The visitors looked off the pace in the early stages in an unseasonably warm day, but came to life with a Kris Commons strike and a Georgios Samaras double.
“Psychologically, the win today gives the players great confidence going into the game”
Neil LennonCeltic manager
Kilmarnock midfielder Sammy Clingan, playing his first game of the season after recovering from a knee injury, reduced the deficit with a free-kick before defender Sean Clohessy made it 3-2 just before the interval.
The home side never really threatened to draw level before Samaras sealed his hat-trick in the 87th minute with a header before substitute Amido Balde, on for Teemu Pukki, scored a fifth two minutes later for his first goal of the season.
Looking ahead to the Champions League Group H clash with the Spanish giants at Celtic Park, Lennon is confident his players will be raring to go, as they look for a repeat of last November's win against the same opponents.
"I didn't think we started the game well at all," said Lennon. "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.
"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 his virus and midfielder Beram Kayal back from a groin strain although midfielder Joe Ledley will miss out with a groin injury.
The former Celtic skipper revealed defender Adam Matthews had to go off against Kilmarnock with a possible virus, which he will monitor.
Lennon added: "Injury-wise we are okay. 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 tomorrow, we are looking a wee bit more vibrant again."
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