A powerful Martin Skrtel header gave the hosts a well-deserved lead at half-time, but Yaya Toure evened things up after an error from Pepe Reina.
However, a Luis Suarez free-kick restored the Reds’ advantage, before Carlos Tevez rounded Joe Hart to score after a terrible backpass from Skrtel.
Brendan Rodgers was encouraged by his side’s display and refused to blame Skrtel for his error in the equalising goal.
“There’s no blame to Martin Skrtel, I’d rather have players wanting to get on to the ball,” he told Sky Sports.
“The courage he has to get on the football and try to play is what is the most important thing.
“It was a brilliant performance I thought. There were a lot of questions asked of the team coming into such a big game but I thought the players were incredible and sometimes the best team doesn’t win, and I think we were the better team.
“From what I’ve seen today, last week was a one-off and today I thought they were terrific.
“The plan was going perfect but then I thought tactically the ability to press at the right time and to drop off and to block was very good. I’m very, very proud of the team,” he concluded.
By Gareth McKnight