With Liverpool two goals up after Joel Matip's header and Salah's penalty, the Egypt forward took possession just inside the Arsenal half and weaved his magic.
Accelerating away from David Luiz and Nacho Monreal, Salah burst into the penalty area and fired home to ensure leaders Liverpool extended their 100 percent start to the Premier League season.
"Mo's third goal was absolutely amazing, but the pedigree of the boys is sensational. Our identity is intensity, and we showed that today," Reds boss Klopp said.
"We had enough bodies and legs to put them under pressure. We had the full-backs really high. The boys did what we wanted them to do and scored wonderful goals.
"It was a brilliant game from my side so early in the season. It was outstanding."
Klopp admitted he was impressed with the way title challengers Liverpool dominated for long periods against an Arsenal team who arrived on Merseyside with two wins from their first two matches.
"The last 10 minutes I saw the possession -- 53 to 47 or something like that -- but over 80 minutes it must have been completely different," he added.
"For 80 minutes we were completely in charge of the game. We are not Disneyland, we do not need to excite everyone in every second."