A last-16, first-leg game low on quality and high on errors saw both teams, with a combined 10 European Cups, struggle to create chances with just three shots on target in 90 minutes.
Sadio Mane had the best two chances for the hosts, screwing a shot wide in the first half and then seeing a stooping header tipped away by Manuel Neuer in the final five minutes.
But, while the frustration grew to levels verging on annoyance in the final quarter of the game, Klopp believes the result is not as disappointing as it may first appear.
“I am pretty sure that Bayern in this moment feels a bit better than we do,” said the Liverpool manager.
“But we have three weeks and day by day the result will feel a bit better for us and a bit worse for Bayern because it’s a 0-0 and it’s the best draw you can get.
“It will be a tough one again to play at Bayern if you need a result. If we had won 1-0 what would have changed really?
“Then a 0-0 over there would have been enough or if we draw 1-1 but that’s now enough as well. So not perfect but good enough.”
Both teams had key players missing – most significantly for Liverpool the suspended Virgil Van Dijk – and Klopp expects things to be different in Munich on March 13.
Despite the dull draw, however, he has not changed his mind about his former Bundesliga rivals.
“I would be really silly if I would have seen weaknesses and I would say now: ‘Yes, (they will have) problems at home’,” he added.
“They don’t have problems, really. We will see who is fit that night, that’s for us important and for them important.
“Bayern had a couple of problems obviously tonight – (Leon) Goretzka I am pretty sure will play that game, maybe Arjen Robben is then fit.
“That could make a big difference as well with his experience, maybe (Franck) Ribery starts.
“So there are a lot of things that can change but we will have a player (Van Dijk) back at least.
“We can play better than we did tonight, so this game is not decided. I don’t think there is any weak team and for sure no team at home is weak, Bayern is not.
“It is not the result or the game we dreamed of. What we wanted was to get a result we can work with and we can work with that result, obviously.
“We still feel like we are proper in the competition but we have to show that in three weeks.”
Bayern boss Niko Kovac was more than happy with the result at Anfield, where Liverpool have not lost in 20 European matches dating back to October 2014.
“I can’t remember that many clubs that have not lost and not conceded at Anfield,” he said.
“Liverpool, they are a sensationally-good team. We didn’t score, but we didn’t let one in.
“We’re at home now and home games are an advantage.
“That’s a great performance. We’ve got the quality and we’ve showed that over recent years but we haven’t achieved anything and I’m the last person to start celebrating.”