Another lightning break from the Reds wrapped up three points in stoppage time, with Salah releasing Mane to round Hennessey and slot into the empty net for his sixth goal in eight league outings against the Eagles.
"I told him "Say to the referee it's not a penalty", said Milivojevic who played for his country at the World Cup finals. As players, we have to respect the referee.
"I'm frustrated because I don't think that's a penalty".
This was a statement win for Klopp's team, installed as City's most likely challengers, and they move into second place after building on last weekend's rout of West Ham.
More importantly, defensively, Joe Gomez put together a fantastic performance in central defense and may just be cementing his spot as a starter, and now Jurgen Klopp's squad has two clean sheets to begin the season.
"I couldn't care less really".
"Over the next three or four years, if Liverpool could win a league or a Champions League, I think Van Dijk has the potential to actually go down alongside Alan Hansen if we're talking about Liverpool's best ever teams - that's how good he is and how good he can become". We know how hard it is to come here, so to win and keep a clean sheet as well, I'm a very happy man.
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It was a step up in opponent; I needed to box and move and still show I can go 10 rounds. And I can tell you first hand he can really wallop.
Right from the start, Salah was in the thick of the action when he surged onto Naby Keita's long pass, but the Egyptian's chip sailed high over the bar.
Klopp's men finally made the breakthrough just seconds before half-time.
Was Oliver correct to award Liverpool the penalty or should it have been disallowed?
Milner, ignoring the sound and fury, nervelessly sent Wayne Hennessey the wrong way with his spot-kick.
Alisson made a fine save to his left to deny Milivojević what would have been a fantastic goal but van Dijk's reaction to the free-kick was a point of comedy for Liverpool fans on Twitter.
While Egypt's Mohamed Salah, who is the talisman of Liverpool's attack was not on the scoresheet, he made major contributions to the Anfield side win. "Mo Salah can play much better, that's 100 per cent", admitted Klopp, adding: "But he was really involved in both goals - decisively involved, so that's two assists, kind of".