Klopp’s side earned a crucial three points thanks to Toby Alderweireld’s late own goal in which Salah was heavily involved.
Last season’s top scorer has failed to find the net for eight games in all competitions but his header was parried away by Hugo Loris before Alderweireld’s mistake.
Roberto Firmino had earlier opened the scoring with a fine header before Lucas Moura restored parity for the visitors.
Liverpool were far from their brilliant best but Salah revealed Klopp instructed his players to get the job done by any means necessary.
Speaking to Sky Sports after the match, the Egyptian said: “When I went into the dressing room, I spoke to the manager.
“I said ‘it’s not always that you have to play good. The most important thing is the points’.
“The big teams always find a way to get the points. Maybe today we didn’t play our top game but winning the game is the most important thing.
“We needed the win to stay in the race and we got it today.”
Klopp appeared to confirm Salah’s words as he praised his side for grinding out a vital victory with an ‘ugly’ performance.
“After Spurs’ goal we started playing again more. We had bigger chances,” the German said.
“We compete with the best team in the world [Manchester City] and play against one of best in the world in Tottenham – it is a tough task. It is all good.
“We can play better football but in the first half we had a lot of good moments. In the second not that many but we scored – 2-1, brilliant!
“City last year were champions and are still pretty good. We have to fight like crazy. The crowd was outstanding.
“They were really here to push us and at the end it helped.
“It is only positive. I said there are 500 ways to win a football game and today was slightly ugly. Who cares?
“I am really happy we don’t have any breaks now. We compete with the best team in world for one position and that is really hard.”