Salah finally got the goal his enterprising display deserved in the 52nd minute, advancing in the area as Arsenal backed off before slotting a fine finish into the far corner.
Liverpool grabbed a point through Roberto Firmino but Klopp said: "Three goals at Arsenal should be enough".
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Liverpool, in their lurid orange away kit, suffered an early blow when captain Jordan Henderson limped off injured.
Firmino had already squandered two glorious headed chances for Liverpool before Coutinho's deft header. Salah's air-kick wasted another Liverpool opportunity and it was no surprise to hear Arsenal booed off at the interval.
In the aftermath of Friday's game, Arsene Wenger admitted that his side had been "frozen" in the first half. Ozil played the ball into Alexandre Lacazette, then took the French forward's audacious back-heel in his stride before clipping a sweet finish past Mignolet.
It seemed unlikely that would be the end of the drama and so it proved as Firmino turned and struck a powerful left-foot shot that Cech could only parry and the ball looped into the net.
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Opting to sit back deep into their own half to negate Salah and Sadio Mane's bursting runs behind their defence, the Arsenal players looked far from comfortable with or without possession.
"I think when you're in position like that, at this level you've got to see the game out", the Englishman told Sky Sports News.
Few of the 59,000 present would disagree.
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Pochettino was delighted with Spurs' comprehensive win over Burnley , but believes they could and should have scored more goals. But it is fantastic for him, " said Pochettino. "It's hard to find words to describe Harry Kane ".