The Hoops headed into the second qualifying-round tie against the Northern Ireland champions on the back of a disappointing run of defeats in pre-season matches so far.
Lennon told BBC Scotland: "I'm delighted. We played well and scored three goals and created a lot of chances.
"Hopefully we have a clean bill of health. It was a sticky game for us and we dealt with it very well.
"A lot of the talk has been about our pre-season and the results but we just wanted to try to get right for these games.
"Some are [getting sharper] and some are still quite rusty, which is totally understandable. But there were a lot of good performances. I'm delighted with the performance and the attitude of the team."
Lennon admits the match in his native Northern Ireland was a special moment for him, adding: "It meant a lot to me personally, bringing a team back home.
"It was a special occasion and I wanted it to be right. I couldn't have asked for any more of the occasion. Both sets of supporters were brilliant."
Celtic were without Gary Hooper, who is the subject of interest from QPR, but Lennon said there was no update on the striker's future.
He said: "There is nothing to add. Talks are ongoing."