The Reds could not breach the Potters' backline on Merseyside, though they had a penalty appeal for handball against Erik Pieters turned down late on.
Klopp was left bemused with referee Andre Marriner's decision but conceded that Liverpool lacked "fluency, fun and joy".
"First of all I take a point, it is positive even if we had more possession and all that, but today was a difficult, intense time for us," Klopp told BBC Sport.
"I saw everything I wanted to see except fluency and fun and joy, it is hard on a day like this. Stoke were a little lucky in some situations.
"We had to make changes, that is always a bit of a rhythm breaker, in the final third everything is instinct between the regulars, and we missed a bit of that. But no-one was seriously injured so we carry on.
"For me it looked a penalty, a clear one. I said a few times in games like this, maybe in the Champions League against Manchester City we were lucky, in the Premier League, not one time. We should have got more penalties, we don't have them.
"But I'm happy how the boys took the game. It was not our best game of course not. And I said a lot of positive things about the crowd, but you cannot only react to what is happening in the game. You have to be on your toes, we can improve that."
Liverpool missed the chance to go second in the table but move four points clear of fourth-placed Tottenham Hotspur.