"It was never in doubt about him being a great player from my side", Klopp said.
Liverpool dominated after the break but Southampton defended tenaciously, even if it was lucky when Maya Yoshida appeared to bring down Keita in the penalty area.
Liverpool now lead City by two points but Pep Guardiola's side have a game in hand.
And captain Jordan Henderson then made sure of the win for the Reds with four minutes to go by turning home a Roberto Firmino low cross, as the Reds went two points clear at the top, albeit having played a game more than City.
This title race is going to go down to the wire and Salah getting back in his old scoring habits can only be a good thing.
"I think if you look at Southampton now, you look at a proper team, a very good outfit that's capable of giving anyone a game and that's the most important thing to see that progression", Bertrand told Southampton's website.
Accruing such a significant total is down to the players' unshakeable belief in their ability to find a way through any opponent, according to Van Dijk.
"There's not many games left, any mistake can cost us".
We have 82 points, that is massive in this insane league and everyone is waiting for us (to slip up).
Henderson proved to be a calming influence for Liverpool after coming on for Georginio Wijnaldum in the 59th minute.
"I think the first half was hard because we made it hard", the No.4, who captained the side from the start, told Liverpoolfc.com post-match.
"We are always going to be risky with the players we have, with the way we play, and you saw it was always going to be hard to defend against us for 90 minutes for them. But I'm still very proud". It's at Anfield, it's a quarter-final, it's a big one for us.
Liverpool head to Southampton in a huge Premier League clash on Friday night, with star man Virgil van Dijk expected to be fit for the contest.
Liverpool would finish the match with 69 percent possession and 17 shots while Southampton only had 31 percent possession and 10 shots.
Last year, Salah was named Professional Footballers' Association Player of the Year and the Football Writers' Association's Footballer of the Year after he scored 44 goals for Liverpool in all competitions.