Of the 47 completed ties that have ended goalless at half-time, 31 (66%) go to the second leg's home team.
"It is not the result or the game we dreamed of", Klopp said at his postmatch news conference.
"It's Monday and we play on Tuesday so most of that should be clear. I thought our performance level was good but we just lacked that little bit in the final third [in the] second half, but first half we could've scored one or two". Unlike a 1-1, then, perhaps 0-0 is as much a 50-50 as you can get when it comes to two-legged knockout football.
The Allianz Arena is a tough place to go and Liverpool will want to take a positive result over there. "So not flawless, but good enough".
But Bayern Munich were too savvy, too streetwise and experienced to fall into the same trap as they frustrated Liverpool at Anfield.
"We made life more hard with the last pass, about 10 or 12 times in a promising position", Klopp said.
The Senegalese put the best chance of the game wide when faced with only Neuer to beat and then shot an acrobatic effort well wide of goal just minutes later.
It was a decently quiet night for Alisson Becker as he only had to make a couple of saves and parries from the Bayern attack.
Mohamed Salah, the man Liverpool look to for moments of inspiration, to create a goal out of nothing, had a night to forget with one of his poorest displays in this competition.
"With the discipline we had in all positions today, it's easier for any defender in the world", Mats Hummels said.
The late flurry that might have been expected of Klopp's men in a bid to establish a sought-after first-leg advantage ultimately never came, with Manuel Neuer's smart low save from Mane's deflected near-post header proving the most either goalkeeper had to do over a laboured final 30 minutes.
Meanwhile, both Klopp and Kovac said their lengthy exchange at the full-time whistle was due to a misunderstanding of pleasantries at the end of a match.
Asked about the confrontation afterwards, Klopp explained: "I wanted to shake Niko's hand immediately".
"I don't know 100 per cent", the Liverpool boss told the club's official website when asked about the three players.
"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. "That's how it was".
"That was amusing. We were on English soil".