Naby Keita's 19th minute goal sealed an impressive away victory for a much-changed Liverpool side.
One man who started the match and played for almost 80 minutes was 36-year-old James Milner. Jurgen Klopp went on to single out the midfielder and underlined his contribution.
The German manager said: "It's difficult to be fitter than Milly. He's a role model. I have told him, I can tell the whole world - nothing we have achieved in the last few years would have happened without James Milner, it's as easy as that.
"Whether he was on the pitch or not, he's set standards in a way not a lot of people can set standards, and it educated all of us."
Milner and his teammates put on a solid display as Liverpool extended their unbeaten Premier League run to 15 games.
Looking back at the match, Klopp said: "It was incredibly difficult for the boys today, to be honest, it's clear. We played two and a half days ago.
"Coming here, a team in form, six home wins on the bounce, great weather, everybody in a good mood, pretty much everything was prepared for another home win.
"The only group who wanted to avoid that was my players. It was an outstanding football game, to be honest. In the circumstances, it was a top-class performance."
Next up for the Reds is the second leg of their Champions League semi-final tie against Villarreal.
Klopp admitted that the team's attention is already on the Spaniards, adding: "We finished the game and our analyst was in the dressing room and I asked him: 'How are Villarreal playing?' They are playing now as well - they were 2-1 down, made a few changes - so that's our life."