Celtic went into a 2-0 first-half lead after Anthony Stokes and Mark Wilson saw their goal-bound shots diverted in via deflections though Lennon says his side were unlucky not to score more.
"I thought the front two set the tone. In the first half they were sensational, we could easily have gone in with a more comfortable lead,” he told reporters.
"At 2-0 you are always concerned that Dundee United could get back in the game, and they did.
"But there was a real belief about the team that they could have got another one, which they did, and really we should have picked Dundee United off a lot better on the counter-attack when they were throwing bodies forward.
"We got a bit of luck with the first two goals but I thought we earned it. We missed easier chances and should have been more clinical at times, but the fact we created quality chances really pleased me.
"I'm really pleased with the threat we have and we defended solidly too."
Dundee United manager Peter Houston was unhappy with the way his side started though was pleased with his team's response in the second-half: "I don't think we turned up in the first half. I don't think we played anything near what we have been doing recently,"
"For some reason we didn't come out the traps and if you give a good Celtic side a two-goal start you are always going to be up against it.
"When your better players can't pass the ball to each other, they are either nervous or Celtic put them under pressure. I felt Celtic put us under real pressure when we had possession.
"Rather than criticise my players, and yes they should have done better, I give credit to Celtic because they did the job properly."