The Merseysiders went into the break 3-0 up, as a Michael Essien own goal and strikes from Jordan Henderson and Daniel Agger but the hosts into a commanding position.
Ramires did pull one back for the west Londoners early in the second period, but a Jonjo Shelvey goal on the hour mark ended any chance of a comeback.
Kenny Dalglish was delighted to end the campaign at Anfield with a win, and feels his side deserved to be victorious.
“I think the players, every one, will be happy that they finished on a high note at Anfield,” the Scot told Sky Sports.
“That performance there is on a par with a lot of the performances that we have had this season but, here especially, we haven’t had the results that the performances have deserved. Tonight we got that.
“Branislav Ivanovic hit the bar early doors, but maybe that’s the luck that you need. We also hit the woodwork twice again, so for us it’s satisfactory and I just hope that the supporters go away feeling very happy.
“I don’t think there is any other place in the Premiership where the supporters would turn up and be as loyal and as supportive as they have been, especially tonight after losing the cup final at the weekend.
“Great credit to them and I hope the boys have put a smile on their face,” he concluded.
By Gareth McKnight