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"Our counter-attacking was pretty flawless, we had some wonderful play", Liverpool manager Juergen Klopp, who was boosted by the return of Sadio Mane after a month out, said. Find out by following our live matchcast.
The 54-year-old Moyes is regarded by the club as the best immediate option to shore up West Ham despite taking Sunderland into the Championship last season, one that ended with him resigning from the club.
The in-form Andre Ayew came into this clash with three goals in his past two outings and he nearly added to that tally in the ninth minute.
Alex Oxlade-Chamberlain also found himself as part of the starting lineup, and the ex-Arsenal man had a fine game on his first Premier League start under Klopp, capping his day off with a well-taken goal.
It could have been oh so different for the hosts who hit the post early on through Andre Ayew, however they were made to pay for this miss as they then suffered a double-hammer blow as Liverpool bagged two goals in three minutes through Salah and Matip.
However, speaking to BT Sport, Klopp explained that the Dutchman had a good night and the swelling had "disappeared" by the time the players convened this morning.
37 million fire extinguishers may not work - Kidde issues recall
It also includes eight push-button models manufactured between 1995 and September 22, 2017. A statement from Kidde reads in part: "customer safety is our first priority".
That duly arrived 15 minutes from time as Salah controlled Mane's pass and rifled a left-footed shot into the bottom-right corner, sealing a marvellous outing for Liverpool and a devastating one for Bilic and West Ham.
Liverpool cut through West Ham like a knife through butter!
Vicente Iborra opened the scoring with his first goal for Leicester before Xherdan Shaqiri levelled.
A 4-1 thrashing at the hands of Liverpool seems to have been the final straw for the club and Bilic, with the Hammers sitting just above the relegation zone heading into the worldwide break. "It's not the first one, it's the second in a row at home".
West Ham got back into the game 10 minutes after the break.
"I have to talk to the chairman, we are going to discuss this defeat", he said.