Ahead of kick-off, Klopp laid out his plan to replace Van Dijk at halftime and introduce Joe Gomez.
But with the level of play in between and Arsenal looking sharp, he refused to eliminate the Dutchman.
However, he was still unwilling to include the center-back for the full game, removing him after the hour mark for Gomez as he opted for a middle ground after being put through another tough test by Arsenal.
The withdrawal of Van Dijk and Salah briefly saw Arsenal come into force after the hour.
But Liverpool settled with solid Gomez alongside youngster Rhys Williams in defense.
Explaining his pre-match selection, Klopp said: “We had to make changes. No chance that all the same players will play again.
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Liverpool started their title defense precariously as they beat a seven-goal thriller against Leeds.
In terms of transfers, the Reds have completed the signing of Thiago Alcantara and Wolves’ Diogo Jota has also arrived, in a shock deal worth a potential £ 45million.
Youngster Ki-Jana Hoever is expected to head to Wolves in a £ 10million deal, while Gini Wijnaldum continues to be linked with Barcelona. There are a lot of things to follow.
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“We kept a few boys who looked really good from a physical point of view.
“Mo (Salah) looks really good so far. Virg (Van Dijk), we will make the change again, if possible at half-time. Virg plays until half-time, Joe (Gomez) after half-time.
“Other than that, you have to see. Well, some players are in slightly new positions, so that’s it.
“James (Milner) has to play left-back again but we’ll see. ”
After a 0-0 draw, the game went to penalties with Arsenal coming out on top.
Adrian saved from Mohamed Elneny as he missed Arsenal’s third kick, but Divock Origi saw Bernd Leno dodge the next penalty.
Harry Wilson then saw his effort saved as he went to sudden death with Joe Willock sending the Gunners.