The Reds failed to break through the League Two outfit's stubborn back-line as they restricted the space available to a youthful side, Klopp admitting it was a "boring" game to watch.
Liverpool had 77 per-cent possession overall but were left frustrated as the Pilgrims, roared on by nearly 9,000 away supporters, held strong to claim a huge result and force a reverse fixture at Home Park later this month that Klopp and co. can ill-afford given their hectic January schedule.
But the German also felt his side ran short of patience too early and made the wrong decisions throughout, which he believes cost them.
Reds boss bemoans team's lack of patience
Asked about Plymouth in his post-match press conference, Klopp acknowledged that it was a "very disciplined performance" and said: "We knew before, when we analysed them, especially the Reading game that they're a good side.
"I think they played differently to Reading, where it was quite an open game. It was not one second an open game today. It was a very dominant game for my side.
"There were no real chances, bar one or two shots, for Plymouth. But they did everything what they had to do to deserve a rematch and now we have it. Yippee.
"It's my responsibility, the whole thing, line-up, performance. We could have done better, 100 per-cent.
"It was really difficult because in the first-half when we had fresh legs and a clear mind, we started well but lost too early the patience. That's how it is.
"Cross in the wrong moment, not crossing in the wrong moment, pass - not really convinced. It was more an opportunity than a real offer. We had all these situations.
"[We were] A little bit unlucky in one or two situations, good goalkeeper saves and then it's 0-0. Not too cool, but not the worst thing in the world and of course deserved for Plymouth."
Playing against a deep-defending team is the hardest think in football, says Klopp
Although Liverpool could not find a way through a defence 68 places lower than them in the Football League ladder, Klopp felt there were still positives to take away from the game.
On centre-back Joe Gomez's return, completing the full 90 minutes in his first senior run-out since October 2015, Klopp continued: "Yeah. Wonderful. But I think it was not the most difficult game in his whole life until now.
"He did well, he's an outstanding talent no doubt. There was a real job to do, a few physical fights and afterwards then a complete change, a big strong guy then a small and very quick boy came on the pitch.
"There was one situation where he [Gomez] struggled a bit in judging the situation.
"I have a lot of good things [to take away]. I know not everyone wants to hear this. That's clear. We are Liverpool, they are Plymouth, but football is like this.
"We tried, even when it didn't look all the time like this. Better decision-making in a few situations and we are completely through. A little bit earlier this, a little bit earlier that, that's how football is.
"The biggest challenge in football is to play a deep defending side, so maybe Plymouth in this moment is happy with the result. For sure they are. They deserved the rematch.
"I don't know if they can play at home exactly the same defensively, probably they can. We will see.
"The crowd was nice, about 9,000. So we're looking forward to it. I tried something today and maybe I'll try it again, we will see."
We didn't give Plymouth the chance to attack, declares Klopp
Plymouth had just one shot on target throughout the 90 minutes and didn't complete, or even attempt, a single pass in Liverpool's box all afternoon.
Asked if he expected Plymouth to attack more than they did, Reds boss Klopp responded: "No. I don't think they could actually. We had the ball all the time. A few counter-attacks, that's it.
"With your own style you create a few things in the game which you have to accept, but you have to use them.
"There was more space than it looked like. There were moments when we lost the game, because then we could have made things differently. We always waited.
"From a specific point of view, we always waited until Plymouth were back again. 'Come on, we wait, and now we start again with passing the ball.' It was boring. It was like this.
"I really am happy that the Liverpool crowd didn't leave the stadium after 60 minutes or something because it wasn't the most exciting game."