Jurgen Klopp's men extended their unbeaten league streak to nine games under precious little pressure, getting back to winning ways after successive draws against Everton and West Brom.
He said: "He's a Liverpool player right now and he's doing really well for us". We have so many things to play for. "But with the squad rotation we have to keep performing".
- Liverpool are the first team in top-flight history to have won four consecutive away games by a margin of at least three goals.
The reigning BBC African Footballer banged in his 20th goal in 26 games in all competitions for the Reds as they produced a dominant performance against their hosts to move up to fourth in the Premier League table.
Coutinho's goal was the highlight.
Liverpool added a second six minutes later when Firmino stopped the ball crossing the byline by hooking it into the six-yard box on the volley for Lovren to finish with a diving header. The Brazilian raced down the left and used teammate Andrew Robertson as a decoy before cutting inside past two players and squeezing a shot inside the post to make it 1-0 after 20 minutes.
Bournemouth played into Liverpool's hands by taking on the visitors and leaving space behind its back four for the likes of Salah and Firmino to exploit.
Oxlade-Chamberlain did the same for Liverpool in the second half before Coutinho curled in an enticing cross that Firmino, potentially from an offside position, ran onto and flicked a header past stranded goalkeeper Asmir Begovic. I try to enjoy the moment.
"We were disciplined, I like how we defended different situations, and our tactical discipline was good".
Bournemouth boss Eddie Howe was left despondent by the defeat and concedes his side are scrapping to stay in the division.
"Against Liverpool, who are so good on the counterattack, you can't turn the ball over like we did today". "We were flat today for whatever reason, we never got going".