Following a cagey opening 45 minutes, Mane looked set to race onto a through-ball down the middle - but referee Paul Tierney elected to blow his whistle to call a halt to the first half.
Klopp seemed perplexed by the decision, while Liverpool fans furiously vented on social media that the whistle appeared to blow six seconds before the allotted - and minimum - one minute of injury time had been played.
Neither side could find a winner after the break, though United went closest through Bruno Fernandes and Paul Pogba as Klopp had Allison Becker to thank for sealing a point for the champions.
Speaking after the game regarding the half-time whistle, Klopp told Sky Sports: "We weren't happy with that, as you can imagine. (It was) strange, very strange.
"I think he's through on goal if he doesn't blow. We were frustrated at half-time but still plenty of time for us to score the goal, but again lacked that quality in the last bit."
While Liverpool's long unbeaten home League run was extended to 68 games, they failed to properly test David De Gea in the visitors goal - and for the first time since March 2005 the Reds have failed to score in three consecutive league matches.
Klopp insists he was happy with the performance as chances are still being created - they had 18 shots but only three were on target - and he is confident the goals will return.
"We have a point more than before the game," he said. "I think the performance was good enough to win it but to win a game you have to score goals and we didn't do that, so that's why we had that result.
"There is nothing fundamentally different, it is just the result is different.
"We try and score and we try not to not score. We have not to worry about it but we obviously have to ignore the fact and hope it will be good again.
"We did that, but the only possibility we have is to create situations and be ready to fail and do it again.
"That is a massive different to when you are flying, because then you deal with the missed chances better.
"I saw my team playing tonight a really good team with a clear idea with super passes and great counter-pressing and great desire to score and we didn't score.
"We will create chances and we will score. It is not as if we decide we will score a goal and now we will do it.
"I will help as much as I can to change the situation."
Additional reporting by PA.