The 31-year-old Egyptian scored in each half to reach 200 goals in English football - 198 for Liverpool and two for Chelsea - and became the first player ever to score in each of Liverpool's first six home games of the season.
"Crazy," Klopp said marvelling about Salah.
"Goal number 200 in England, right? Exceptional, played a super game today," Klopp added. "Two players always around him, he kept the ball.
"We had so many good moments first half. "(The) composure for the first goal is insane. No doubt in that area, you see it on the scoresheet. Special player."
Liverpool have yet to lose at their Anfield fortress this season in all competitions, winning their sixth successive league game there on Sunday.
But while Klopp was thrilled with the performance he had strong words for the schedulers who have pencilled in their next game against leaders Manchester City as a 12:30pm kick-off at the Etihad on November 25th, right after the international break.
"How can you put the Man City game on at 12:30?" he asked reporters after the game. "These people don't know football.
"There could be a moment when these two teams have 30 international players, we pick up the South Americans on one plane to arrive here."
Klopp was happy with his team's bounce-back after their 3-2 loss at Toulouse in the Europa League group stage on Thursday.
"I'm very pleased to use that opportunity ... to lose against Toulouse and then react in the way we did today," he said.
