But Salah limped off when he was substituted on 83 minutes following his match-winning salvo, casting him as a doubt to face Burnley in less than 48 hours' time on New Year's Day.
Asked about the free-scoring winger's fitness, Klopp told his post-match press conference: "I don't know in this moment exactly [what his issue is] but he was limping. That's never a good sign."
The German admitted that they "have to see what his [Salah's] problem was" and analyse it from there, insisting that they "will see what he can do for the next game" against the Clarets.
Liverpool boss confident Salah can keep up current form
Though he wasted first-half opportunities to put Liverpool ahead, the 25-year-old never allowed his intensity and determination to drop after those misses, his second-half display helping the Reds to cash in on their domination.
On whether the winger can continue such a rich vein of form in the first-half of the campaign going into the New Year, Klopp declared: "He can keep that standard, for sure.
"He is still a young player, he can improve. It's not about scoring only, it's about other situations as well. He's so important for us.
"But he knows and I know that he couldn't score if he didn't have the fantastic support of all the other boys," continued Klopp, hailing his side's "fantastic passes" such as "Sadio's idea in the moment before Mo scored the first goal."
"I don't think a lot of people in the stadium saw that it would be an opportunity. That was really important," he explained.
Klopp: Reds' reaction was "cool"
Klopp continued to hail Salah: "I think he can keep the standard but that’s normal. All the boys can keep the standard they have in the moment. It's not that it’s only a run.
"The boys show their quality. We did that already a few times, the thing is more to get the results. That's what we did tonight. To get this result, the most important thing was the defensive performance."
Klopp explained that he is "really happy about the concentration level in all defending moments" because Liverpool's back-line "were spot-on and aggressive in a very legal way."
He acknowledged that their bookings, in particular Emre Can's yellow card for an altercation with Harry Maguire after Salah's first goal, "were not necessary" but felt that they "showed the desire of the boys to turn this game."
He added: "I was not happy about the yellow cards but the reaction was cool. It was a good team performance tonight."