Mohamed Salah and second-half substitute Roberto Firmino netted doubles, while Sadio Mane was also on the scoresheet in Portugal.
The result sees the Reds stay two points clear of Atletico Madrid at the top of Group B after two rounds of matches.
Read on for a transcript of Klopp's post-match press conference...
On what pleased him most about the performance…
That we had a tricky start because obviously Porto watched the Brentford game, started pretty direct. We struggled a little bit in the beginning but that's the reason why we didn't make a lot of changes, that's because I wanted that we find the feedback on the pitch and sort the situation there and that's what we did. From a specific moment on we played really good football. We didn't use our big chances, we used two half-chances to score, to be 2-0 up. But we had really good football moments, we played good against a side who were fighting obviously for some parts of the game because they lost a centre-half after, or in, the Atletico game and the other centre-half today after warming up. We know best that things like this are not helpful and when you play then against us it's even worse. So, we used that. But we played, really, some good football and scored nice goals, but had even better chances. So, it's all good for tonight.
Highlights: Porto 1-5 Liverpool
On Curtis Jones' performance…
Curtis played a good game. He had some problems a little bit with the stomach before the game; they told me I need to keep an eye on him but I told him after the game whatever it is, keep it because it was really a good game. He played a really good game, he was everywhere, he was involved in everything. Set up the first goal with a surprising finish, goalie cannot save it. In a lot of other situations he was really there - maybe not as spectacular as the offensive stuff, but defensively he played a top-class game. He defended really well, pressed from the blind side, a lot of things I liked a lot about his performance tonight. So, let's keep going, Curtis, it was not bad tonight.
On what the current run of form does ahead of Sunday's Manchester City clash and scoring 20 goals in September...
Unfortunately, it didn't feel like that, but thank you for telling me! We conceded as well some or a few. We play against Man City, I don't think now it makes too much sense to think too much about how many goals we can score against them. We need a complex and complete performance against them to have a chance only and that's it. But I'm really looking forward to it, I'm looking forward to playing at home again after a while. We have to work hard, we had to work hard in all the games we had - tonight, last Saturday, which is only three days ago, it's really tough. But now we have two days more to the City game, which will be helpful, and then we will be fresh again and then give it a go. That's it.
On the situation with Trent Alexander-Arnold...
So the situation when you play Saturday and Tuesday, the players who start the game - which Trent obviously did - have on Sunday no training, they have recovery. On Monday, the only session we have together, we pretty much walk through the things. We have meetings and on the pitch we just show the difference between the opponents, so there was no intensity really in the session. But Trent anyway in the middle of the session felt his adductor and in that area he has now a little injury. Obviously when you have something with your muscle, it's not likely for Sunday - no muscle injury heals that quick. After that, it's internationals. I don't want to make the decision for him but what I heard, I don't think it will be possible for him to be with the national team - but the other people have to decide that in the end. But hopefully after that he will be ready again, but we don't know exactly.