Lucas Leiva's first goal since September 2010, a header from Philippe Coutinho's left-wing corner, proved to be enough to book a fourth-round tie at home to Wolves.
Klopp felt his side could have won more comfortably, with Divock Origi seeing a late penalty saved by Plymouth captain Luke McCormick, and that Liverpool should have had another spot-kick when Daniel Sturridge went down in the box.
"The longer you don't score the more exciting it can get and you saw that when they started getting really direct, we are not used to it and they hadn't played too often together - the back-line," Klopp told BT Sport.
"Okay, they had a few chances but so did we, especially in the last 20 minutes where we controlled the game. Maybe it wasn't the most exciting game but for us it it's very important as it's another game for a few of the young boys, so that's all good. I love this in football, that everyone can cause everybody problems.
"It was a clear penalty in the first half and that would have helped because this team had not played together too much. You could see the team were looking around like they were embarrassed to be losing challenges against a fourth division team.
"In the second half it was good, but then it became a bit static. We had a penalty, and 2-0, 3-0, 4-0 would have been okay, but 1-0, I'm fine with that. I was not too concerned about going through, but I thought 'oh my god another 30 minutes', but it is all good, no extra time, job done, let's go home. As nice as it is here, we leave as early as possible, so all good."
Lucas had not scored since a Europa League tie against Steaua Bucharest, but Klopp said the Brazilian nets regularly in practice sessions.
"Every week in training we play old versus young," Klopp said. "He is a top scorer for old, which is unbelievable."