However, Salzburg did the unlikely and got themselves back on level terms with half an hour to go as Hee-Chan Hwang, Takumi Minamino and Erling Haaland all scored for the visitors.
Despite the Reds looking lacklustre during the second-half, they found themselves a winner as Roberto Firmino's flicked header was met by Salah, who finished past goalkeeper Cican Stankovic to give Liverpool all three points.
Speaking after the game, Klopp pointed out the issues he saw from the touchline, suggesting the Reds were too one-dimensional in midfield after the break, allowing Salzburg to counter them effectively.
"How do I explain that? I think it was obvious: we left the very successful path of the first 30 minutes. That was some of the best football we played so far, against how we all saw a little bit later a very well organised team with a clear idea and identity," he said.
"We did everything they don't like, on a high speed, scored the three goals, could have scored more. They changed the system – that's allowed and is not really a problem usually, but tonight it was for us because we changed the approach a little bit for some reason.
"Some were in a controlling mood, some were in an attacking mood, other positions were too hectic.
"The main problem was that we tried to finish our situations off through the middle of the park; they had one midfielder less in the defensive [area] because they took a bit more risk and left a No.10 in between the lines.
"So they had one midfielder less and we still tried to push through the centre. We lost the balls there, they passed the ball to the No.10, he could turn at the back of Fabinho, could turn and counter-attack.
"That changed the momentum of the game.
"We opened the door and they were running through, chasing through the door. They scored their goal, then at half-time we tried to adjust but all the goals they scored – first goal, we lost the ball easy; second or third goal, we lost the ball easy.
"Counter-attacks, when you are 3-1 up, makes not a lot of sense. But it happened. It was a very important lesson for us tonight, but I prefer massively to learn it in the game than after the game because if we would have lost 4-3 it would have been the same lesson.
"But now we won 4-3, so three points and a lot to learn from. So I'm fine. I knew before we have to improve a lot, now everybody knows it. That's OK. We made it more intense than necessary but we sorted it result-wise.
"Three points in the group, game on, so now recover and face Leicester."
Meanwhile, goalscorer Robertson also believes the Reds can learn from their mistakes, admitting they "got a bit complacent" after going three ahead.
"It's a tough one to put your finger on," he said.
"You've got three points in the Champions League and that's not easy to do against whoever you're playing. Salzburg are a good team but we have to be disappointed with probably the last 60 minutes of how we played.
"We allowed them back into it and we don't usually do that, especially at home. We're very good at killing off teams and when we're 3-0 up we then control the game, which we never done.
"We got a bit complacent, we started giving passes away where we shouldn't have, started getting a bit sloppy.
"We need to look at that because that can't happen, but like I said, we can't be too negative on ourselves - we got the three points and now this campaign's up and running for the Champions League."