Klopp’s side travelled to Dean Court in high spirits after their historic 7-0 thrashing of arch rivals Manchester United last weekend.
But Liverpool’s hopes of using that remarkable result as a springboard to push for a top four finish in the Premier League were given a brutal reality check on the south coast.
Philip Billing punished woeful Liverpool defending to put the struggling hosts ahead early on and Salah blew the chance to equalise when he fired wide from a second half spot-kick.
Salah became Liverpool’s record scorer in the Premier League era when he netted twice against United.
But the Egypt star’s failure to add to his total of 130 condemned Liverpool to a first defeat in their last six league games.
Fifth-placed Liverpool appeared to use up all their goals in the United demolition and their toothless display left them three points behind Tottenham ahead of the north Londoners’ game against Nottingham Forest later on Saturday.
“There is a lot to go for but today is not the moment to talk about that,” Klopp said.
“This game was a massive knock. You know how it is with knocks, you have to take them and see how big the scars are and go from there.”
Apart from the damage done to Liverpool’s top four bid, it was hardly ideal preparation for Wednesday’s Champions League last 16 second leg at Real Madrid, where the Reds need a miracle in the Spanish capital to overturn a 5-2 deficit.
Losing to a Bournemouth side that started the day bottom of the table and lost 9-0 at Liverpool in August was the latest indignity in a troubled season for Klopp’s men which has featured shock losses against Brighton, Brentford and Wolves.
Liverpool have won just three of their 13 games away from Anfield and Klopp said: “Concerned? Yes, I see it.
“It was a big strength for us in the last year, it made a real difference, but that is how it is.
“We get a penalty, miss the penalty and it looked a little bit for me that if we score there it would give us a proper boost but we didn’t. It’s very frustrating.”
Liverpool’s Virgil van Dijk went close to an early opener with a header that was arrowing towards the top corner until Bournemouth midfielder Jefferson Lerma cleared off the line.
Bournemouth should have capitalised on that escape moments later when Dominic Solanke’s pass sent Dango Ouattara clean through on goal.
But as Ouattara rounded Liverpool keeper Alisson Becker, his touch took him too wide and he could only shoot into the side-netting.
Liverpool’s high defensive line was creaking and Ouattara finally helped puncture it in the 28th minute.
Racing onto a pass down the right flank, Ouattara shrugged off Van Dijk’s weak challenge and whipped over a low cross that Billing finished from close-range as Liverpool’s sluggish defenders failed to react.
Van Dijk had a chance to make amends for his part in Liverpool’s shambolic defending when he climbed to meet Robertson’s cross, but the Dutch centre-back headed wide with the goal at his mercy.
Klopp responded to Liverpool’s lethargic performance by sending on Diogo Jota for Harvey Elliott at half-time.
It took just three minutes for Jota to make his presence felt with a curler that Neto pushed away at full stretch.
Jota was the catalyst for Liverpool’s 69th minute penalty.
Picked out by James Milner’s cross, Jota rose highest at the far post for a goal-bound header that was blocked by Adam Smith’s outstretched arm.
The spot-kick was awarded after a VAR check, but Salah let Bournemouth off the hook as he blazed his effort woefully wide.