The Reds got off to the perfect start when Salah netted twice in the first half to send them on their way.
Sadio Mane grabbed the third before Roberto Firmino scored twice to seemingly put Liverpool out of sight.
But after going five goals to the good, Klopp’s men conceded two late goals.
Edin Dzeko made the most of a Dejan Lovren mistake to pull one back, before Diego Perotti scored from the penalty spot.
And despite Klopp being all smiles during Liverpool’s early rout, defensive mistakes were clearly at the forefront of his mind come full-time.
“Long term perfect performance for pretty much 80 minutes or so,” Klopp admitted.
“We made defensively one mistake.