The newly promoted side have proven to be very organised so far and were unfortunate last week at Old Trafford, only losing thanks to an unfortunate own goal against Manchester United.
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The in-form Mohamed Salah added two more goals to his impressive tally, and Sadio Mane also got on the scoresheet.
A comeback would never come for Brighton, as Coutinho put the final nail in the coffin for the Seagulls three minutes before full time.
A corner from Coutinho corner found the head of an unmarked Can, who leapt to met the ball, and his powerful header flew past Matthew Ryan to give Liverpool the lead.
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A second opportunity fell the way of the Brazilian in the 11th minute but despite the ball falling invitingly for him, the forward drilled the ball harmlessly into the stands.
Can's performance was encouraging but it was hard to say on the basis of this whether he could tide things over for the Liverpool defence while Matip is out.
Philippe Coutinho produced another moment of brilliance as his free-kick helped Liverpool to a thumping 5-1 win at Brighton. "It's unlikely he will be involved at Brighton but we'll see". We are not the only team of our level who have been on the back of a big defeat this season. "They were always going to have more possession, but after 30 minutes we had had the best chance - and then within two minutes we were 2-0 down".
After joining from Roma in the summer, he has already scored 17 goals in all competitions and is the Premier League's leading scorer with 12 goals.
Coutinho rolled a cheeky free kick under the defensive wall and into the net for 4-1 in the 87th, before sending in the shot that Brighton defender Lewis Dunk deflected into his own net to complete the rout.
David Moyes "really relishing" West Ham United challenge
He impressed under Westley so much last season, he was included in the Pre-Season Tour this year and hasn't been seen since. Moyes will be expecting a committed performance and, if he gets one, I don't think West Ham will leave empty-handed.
President Trump talks briefly on tax reform, North Korea
Mike Rounds on what exactly is happening while entering senate chamber: "We're going to go in and find out what's going on". Later this week, the full Senate is expected to vote on the bill that would benefit the wealthiest Americans and Mr Trump.
Sevilla draws after Liverpool wastes 3-goal lead in CL
The Reds will travel to the Ramon Sanchez Pizjuan stadium under pressure, with just a one-point advantage over Sevilla in Group E. Coach Eduardo Berizzo delivered a rousing team-talk at half-time and it had the desired response.