Shaqiri was pivotal in Liverpool’s first and third goals at Anfield on Saturday but was unable to build on his first-ever start for the club, having been withdrawn for James Milner at the break.
Van Dijk, meanwhile, was forced to come off early in the second half, heading straight down the tunnel before emerging to watch the rest of the game from the dugout.
“He had already, before the PSG game, kind of a bruise on the ribs, which is very uncomfortable,” Klopp said of his centre-half at his postmatch news conference.
“Today he had another hit there. It’s not cool, but should not be too serious. He said: ‘I couldn’t shout anymore,’ so that’s obviously 60 percent less of his level. But he should hopefully be OK. I didn’t hear anything different.”
On Shaqiri, Klopp said: “I said to Shaq in half-time, I’ve never taken off a player after such an influential time without an injury.
“He was not injured. I wanted to control the game, go back to our normal formation. That helped and we could be more controlled.
“It was not easy, to be honest. It’s my job to sometimes deliver news that nobody wants to hear.
“That’s how it is in half-time. He’s a fantastic boy and I explained it to him, so it’s no problem. Usually I don’t explain substitutions at half-time, but I thought today it makes sense.
“It’s just good to have him. You saw the free kick was outstanding. What a ball. The whole team was not used to what we did today and, as a new player, usually you struggle most. But he didn’t.
“He tried everything. We only had problem in defensive [situations], offensive it was a good idea. We have to work on that with him more often. He was good. I liked it.”
Liverpool made history in Klopp’s 600th game in management as they have now won their first seven matches of a season in all competitions for the very first time.
A Wesley Hoedt own goal opened the scoring at Anfield inside 10 minutes before Joel Matip later doubled Liverpool’s lead. Mohamed Salah then added the third to end his three-game run of not scoring.
“I lost seven games in a row once, that felt different,” Klopp, who watched his side reclaim top spot in the Premier League, said. “But then we won game No. 8 5-0, very cool.
“It’s a surprise, but all the performances we showed so far were good enough to win the games. Different challenges, different styles of opponent, the boys were there, really in the situation and in the game.
“That’s good, but the next one is coming. Coming on Wednesday then Saturday then Wednesday again, and then the period ends with a nice game against Man City. It will be tough, but for all of us. I am really sure we are mature enough to understand it.”