The Reds' continental campaign ended at the quarter-final stage with a 3-1 aggregate defeat to Gian Piero Gasperini's side, whose 1-0 loss in Bergamo proved inconsequential thanks to their 3-0 Anfield triumph in the first leg.
Liverpool travelled to Italy with memorable comeback wins over AC Milan and Barcelona already under their belts, and their latest bid for a spectacular turnaround began strongly, as Salah crashed home a seventh-minute penalty after Matteo Ruggeri's handball.
However, the 31-year-old then squandered a magnificent chance to put Liverpool two goals up at the Gewiss Stadium, as he beat the offside trap to latch onto Cody Gakpo's ball over the top, finding himself one-on-one with Juan Musso.
The Atalanta goalkeeper was in no man's land, and Salah would ostensibly have the simple job of lobbing the goalkeeper into an empty net, but his attempt bounced the wrong side of the post.
Klopp refuses to make "big story" of Salah miss
From that point on, Liverpool were toothless in attack against La Dea, carving out just 0.11 Expected Goals (xG) in the second half, in which Salah was substituted with just 65 minutes on the clock.
The forward has now been sacrificed early twice this month - he was withdrawn on the hour against Sheffield United in the Premier League on April 4 - but Klopp told his post-match press conference that Salah is simply experiencing what all strikers experience.
"I am not particularly concerned. That's what strikers do, that's what happens to strikers, that's how it is. We have to go through this, he has to go through that," the 56-year-old said.
"He is one of the most experienced players we have in the squad. We will go through that but that's pretty much all. It's not that Mo didn't miss chances before in his life, that's a part of the game.
"The penalty was super-convincing, a super penalty, then the next chance, that was obviously unlucky but it is not the first time he missed a chance like that. I will not make a big story of it, what you make of it I obviously have no influence on obviously, but no, I am not particularly concerned."
Klopp admits key man was "running out of gas" in second half
Despite the plethora of second-half changes, Liverpool's meek second-half display was in stark contrast to their explosive first-half performance, where the returning Trent Alexander-Arnold was pulling the strings on the right.
Making his first start since picking up a knee injury in February, it was the right-back's cross that Ruggeri blocked with his hand for Salah's spot kick, but his influence waned in the second period, and he was taken off just after Salah.
Klopp conceded that Alexander-Arnold "running out of gas" was a big factor in Liverpool's failure to keep up the tempo, but he lavished praise on Alexis Mac Allister for his "crazy" and "insane" ability to make it through the match in the number six role.
"Look, the biggest problem for us in the second half was that we couldn't keep that tempo. For us, you saw tonight in Trent Alexander-Arnold which player we didn't have for a while now," Klopp added.
"As long as he was fresh, together with Macca [Alexis Mac Allister] he set the tempo, the rhythm, the direction of the game. Obviously he was a bit running a bit out of gas. Macca had to go through this game, which is crazy and the way he did it was absolutely insane, but that was the difference."
Having missed out on a semi-final showdown with French giants Marseille, Liverpool now only have the Premier League left to fight for and return to top-flight action away to Fulham on Sunday afternoon.