Liverpool set up a fourth-round tie at home to Wolves with old head Lucas Leiva scoring a rare goal in their 1-0 win at Home Park.
Klopp named a stronger side than he had done in the goalless draw against the League Two high-fliers at Anfield 10 days earlier, but four teenagers still started the third-round replay – Trent Alexander-Arnold, Joe Gomez, Ovie Ejaria and Ben Woodburn.
“It was tough again, but we did better than Anfield in the right moments,” Liverpool manager Klopp said. “There were a lot of challenges for the young players.
“We were playing live on television against a fourth division team and everybody thinks you are three or four classes better.
“You do not want to feel the embarrassment of losing a game like this.
“I thought I could see that a bit when it started happening to them in the first half.
“I thought at half-time we could fix this, and we were kind of back in the race and controlled the game well after.
“I’m happy about their potential and we will do everything we can to let it grow. But they have big job to do, too.”
But Klopp said: “He played in an old-against-young match last week when we finished training and he was top scorer.
“I was really surprised he didn’t score for that long. But he has a great personality, is a good player and a really good guy.
“Sometimes you have to line up without him, and it’s not his hobby to accept this. But he’s okay and really important for us.”
Plymouth almost forced the tie into extra time when Jake Jervis volleyed against the post 15 minutes from time.
After being criticised by some for being ultra-defensive at Anfield, when they had only 23 per cent possession, Plymouth had some good moments and Liverpool were never allowed to rest easily.
Plymouth manager Derek Adams said: “Over the two games we are very proud of the performance. But it was not our night with Jake hitting the post.
“You’re disappointed when you go out of the cup, but Liverpool have been very respectful playing the players they did tonight and we pushed them all the way.
“We’ve put Plymouth Argyle on the map again, the support we’ve had over the two games has been fantastic.
“We’ve shown a worldwide audience we can get back to where this club feels it belongs – and that is in the Championship.
“There is a population of 300,000 here – the biggest city not to have had a team in the Premier League – and we’re building the blocks to move the club through the leagues again.”