His act of humility went down a storm with Liverpool fans, as did the hat-trick.
Cook's day then went from bad to worse when he inexplicably backheeled a terrific own goal past his own keeper to make it 3-0 to the Reds.
Liverpool, now enjoying their best start to a domestic season having accrued 42 points from their opening 16 games, moved top of the Premier League with the victory, one point ahead of Manchester City who face Chelsea later on Saturday.
Still, the Egyptian refused to take his man of the match award whilst being interviewed alongside Milner after the match, tellingSky Sports: "No, no". The first one, it is a foul actually but he wants to score the goal so he stays on his feet and scores it.
And it wasn't just Milner who was singled out for praise, with Salah having bagged three goals to take him - since the start of last season - within just one strike of Barcelona star Lionel Messi.
Liverpool struck just when the hosts were enjoying their best spell, though, as Asmir Begovic failed to hold on to Firmino's long-range shot and parried the ball out into a unsafe area, where Salah was waiting to tuck home the rebound.
Speaking to reporters after the game, Klopp admitted that he could see little room for improvement in his side's second-half display, though he stressed that they took time to find their "rhythm" before the break.
City will have the chance to overtake Liverpool later on when they take on Chelsea at Stamford Bridge.
The Reds leapfrogged Manchester City in the early kick-off.
Klopp's side will now face a must-win game against Napoli on Tuesday night before welcoming bitter rivals Manchester United to Anfield next Sunday.
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