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Swansea manager Michael Laudrup rested a host of regular starters with next weekend's Capital One (League) Cup final against fourth-tier Bradford City in mind, a decision which spectacularly backfired.
"I wanted to leave a few out but that's not an excuse, we could have lost 10-0. We are all to blame, starting with me and the players," Laudrup said.
"It was a nightmare, we got slaughtered out there. First half we were still in the game but to give away three goals like that in 10 minutes at the start of the second half was terrible, we have to say sorry to the fans."
Steven Gerrard's penalty on 34 minutes set Liverpool on their way, the midfielder making no mistake having had a spot-kick saved in the home defeat by West Bromwich Albion on Monday.
Coutinho, who joined last month from Inter Milan on a long-term contract, ran at the Swansea defence and beat keeper Michel Vorm soon after the restart to make it 2-0 as Liverpool quickly settled the game in a rampant spell.
Coutinho was also involved in the build-up in Liverpool's third goal four minutes later, linking up with Luis Suarez before Daniel Sturridge crossed for Jose Enrique to prod in.
Suarez hit a fourth on 56 after twisting and turning in the area before Sturridge made it 5-0 with a second penalty.
It was Liverpool's first victory over a team in the top half of the Premier League this season and a first for manager Brendan Rodgers over his former side.
Victory came at a cost for Liverpool after Italian striker Fabio Borini suffered a suspected dislocated shoulder and will miss the rest of the season.
Borini's first season at the club after joining from AS Roma last July has proved difficult. He has scored just once - in a Europa League tie - and was out for over three months between October and January after sustaining a foot fracture.
"It looks like Fabio Borini has a dislocated shoulder which will keep him out for the season," Rodgers said.
"He did a similar one at Chelsea on the other side. It's a big blow for us."