Reds boss Rafa Benitez was full of praise for his side's character.
Fernando Torres' two goals were sandwiched by Pablo Zabeletta's red card with Dirk Kuyt hitting an injury-time winner.
"I think it was a good game, especially for our fans. In the first half we made too many mistakes," he told Sky Sports.
"We changed things around in the second half. At half-time I talked with them about scoring the first goal.
"We were sure we could get back in the game. When you're not playing at your level it's important to show character."
Torres' brace was his fourth goal in two league outings following his slow start to the campaign.
"I don't think he's changed anything. He's on fire now, which is good," he continued.
"The main thing for me was the work rate of the team."