The Hoops fans were silenced when Melvin de Leeuw fired the visitors ahead, and although Kris Commons equalised from close range the Highlanders were worth a point.
Lennon said: "We were a wee bit flat. I totally understand that. The game was an aside to the celebrations really.
"We had no preparation for this at all and you could probably see that by the way we played, but overall I am not angry or disappointed or anything like that.
"We will play better between now and the end of the season that's for sure.
"When we get the trophy that will be another day of celebration and quite rightly so.
"I think the players made plans for this evening and some of them might have had half a mind on it before the game.
"But they deserve it and we are still looking forward to the remainder of the season, where I am looking for six wins if we can.
"We might change the shape of the team as we go along as well, I will look at
different aspects of the way we want to play. I want a bit more vibrancy in the
next six games."
Lennon was able to give a debut to 18-year-old defender Eoghan O'Connell while 17-year-old Liam Henderson made his fifth appearance.
"Eoghan did very well and grew into the game and got better and better so I was very pleased with his contribution, and Liam as well," Lennon added.
"It was his fifth appearance and he played with great maturity for someone of his age.
"I am excited about the likes of Liam and Eoghan coming through, but I would like to finish the season on a high and we will do that."
County boss Derek Adams added: "I thought we were better than Celtic today, that's the way I look at it.
"You've got to be happy coming here and taking a point, it's a difficult place, but you become greedy at times.
"I'd have taken a point before the game, but after it I'm disappointed we haven't come away with three points.
"Celtic didn't really create much, they had a lot of possession, but I thought
we should've won the game."