Despite 26 corners and numerous efforts on goal, the Hoops could not find the back of the net and they were punished when Dougie Imrie converted a 97th-minute penalty.
"I have got to be philosophical about it," said Lennon. "It wasn't for the attitude or want of trying in the game.
"It just wasn't our night for whatever reason. The only disappointment for me is we had 26 corners and we didn't convert one of them with the height we had in the team.
"We have to take our chances. We ended up putting Virgil van Dijk up (front) to give us something different and certainly we created a lot more."
The Northern Irishman continued: "If you don't take your chances you don't expect to win the game.
"I thought we would at least get one tonight and that is a surprise and disappointment to me.
"But I am not going to hammer the players, it has been a very demanding start to the season for them and I think they are looking forward to the game on Saturday.
"It is a frustration but I will get over it very quickly. I have too much to look forward to, to dwell on it."
Morton boss Allan Moore, whose side sit second bottom in the Championship, described the result as "incredible".
"There aren't many times I've come here even in my playing career and got good results," said Moore.
"But to a man we were excellent, especially after the league form we've had over the last couple of weeks. What a dressing room it was, that's why you come to play football.
"They were talking before the game about swapping tops with the Celtic players. I told them if they swap it to make sure it was full of sweat.
"If they did that, they'd have put a shift - and to a man they did that. I'm over the moon and hopefully it's the catalyst to kick on in the league."