But Liverpool responded quickly enough to ensure panic and nervousness wouldn't set in - temporarily, at least - with Salah controlling Emre Can's through ball before drilling it past Nick Pope in the Burnley goal three minutes later.
Burnley has picked up away points at three of last season's top-six teams, beating Chelsea on the opening day and drawing against Tottenham at Wembley.
But it is hard to blame the supporters for the anxiousness when they repeatedly see a match of this type numerous times under Klopp. They should have won the game, yet they could easily have lost it despite dominating from start to finish.
The Senegal worldwide took a three-match ban and Coutinho looks the ideal replacement, having operated in the same left-sided role for most of last season. I trust people until they give me an opportunity or a possibility not to trust them anymore. My job is to see the performance and we reacted really well.
Klopp admits he is upset, but won't panic after dropping two points.
It was, as Tarkowski, linked up with Brady who headed across the edge of the box, helped by a Chris Wood touch onto an unmarked Arfield who eased the ball past some questionable defending to steer the ball past Simon Mignolet. Left badly exposed for the goal, but he's no doubt used to that by now.
A second for the hosts looked a matter of when rather than if, but it never did arrive. Hesitation by centre-backs Joel Matip and Ragnar Klavan allowed the ball to drop between them in the middle of the penalty area.
"Just to cool the people down, what if the new player doesn't hit the first ball [like Dejan Lovren against Sevilla] and he makes exactly the same mistake?"
Contrasted with their opposite number, who amassed five shots with only one off-course and it shows just how badly Klopp's side are missing Mane.
He leaves one of our most expensive transfers on the bench for James Milner. This made a lot of his shots appear as if they're passed directly to the keeper, as was the case against Manchester City as well. Daniel Sturridge had seven attempts. Nicolas Otamendi added a fourth in the second half with a close-range header.