The Brazil international started for the first time since November following his recovery from injury and set up the only goal at Home Park.
Coutinho showed to be well on the comeback trail following the knock to his ankle as his 18th-minute corner was headed in by Lucas Leiva.
The star managed just over an hour of action before being withdrawn, and Klopp saw plenty of reasons to be optimistic following his display.
"I'm happy, really happy. It was very important for us," the manager told reporters. "I thought 60 to 65 minutes was the perfect intensity for today. Good for him and good for us."
Divock Origi missed a late penalty for Liverpool at Home Park, but his team managed to come through their third-round replay.
Teenagers Ovie Ejaria, Ben Woodburn and Trent Alexander-Arnold started, while Sheyi Ojo and Harry Wilson came off the bench.
"I saw a few really good things but they still have to learn," Klopp said of his youngsters.
"We are not here to celebrate each single performance of our young players – that's what we expect, that's why they play. And then they need to get ready to be criticised.
"I don't care what you say, but it's important that they really listen to what we have to say.
"I liked, for example, the reaction of Ojo tonight. Everybody, maybe, with Ojo involved they expected he would have started if he was in this game tonight as one of the young players, but I was not too happy with one or two things.
"That's not to say, it's about something you need to feel and then go again. Today, I thought he made a big difference when he came on, with his speed and there was sharpness involved. He's a wonderful player but, without sharpness, it's nothing.
"I'm happy about their potential and we will do whatever we can to let it grow but they have a big job to do, too."
Liverpool are back in action in the Premier League on Saturday, hosting Swansea City.