Having scored against Chelsea for Basel in 2013, Salah achieved this feat when he put past Sevilla at Anfield (qualifiers excluded).
More good news from Klopp came from the fact that Lallana's club teammate Alex Oxlade-Chamberlain also received his first call up to the national side since October, a move Klopp believes is a deserved one.
Salah, 25, struck four goals in Liverpool's 5-0 thrashing of Watford that lifted them back into third place in the Premier League on Saturday.
In the 27th minute, Liverpool were forced into an early change as Emre Can went off injured and was replaced by James Milner. He couldn't get near him on the ball or off it. At least without possession he was just left standing around looking kinda gormless - although when Salah hit him with that bodyswerve on the first goal, the Uruguayan collapsed like a Jenga tower.More news: O rasto do tornado no Algarve
He is on top of the scoring charts in the 2017/18 league season, four clear of second-placed Harry Kane of Tottenham Hotspur.
At one stage on Saturday evening Klopp could be seen applauding after Salah chased back towards his own half, one of his few attempts at adding something defensively to Liverpool's cause.
"We've lost once and we've won once against them in the league". Mane was runner-up. "You need always in a game somebody who brings the ball over the line". And that worked nicely.
Watford had decent spells in the first half and Roberto Pereyra did strike the crossbar with a second-half free kick, but they were easy pickings for Klopp's slick side.The defeat left Watford in 11th spot, a comfortable eight points above the relegation zone.
Klopp is right in saying that no player truly likes to be compared to Messi, because the Barcelona galactico might be the best player in the world right now, and such comparisons inevitably bring ridiculous expectations.More news: Russians vote as Vladimir Putin seeks tighter grip on power
He made the right changes after the setback at Manchester United and ensured his side's reaction to adversity was swift and brutal.
The former Dortmund coach admits that he has been taken aback by just how successful his summer signing has been playing through the middle of the attack.
"If the question is what do I think about his performance, I think it's quite exceptional", Klopp said afterwards.
He scored in all four of Liverpool's fixtures during February.More news: Abbas calls United States ambassador to Israel a 'son of a bitch'