Fernando Torres scored in the first half as Liverpool ran the game with embarrassing ease, but Derby's spirit after the break saw them equalise through Jay McEveley, and Liverpool were hanging on at the end.
It got so tense that rival managers Paul Jewell and Rafael Benitez exchanged heated words on the touchline after McEveley was booked for a foul on Andriy Voronin.
Benitez said: "Paul Jewell had a different view of the incident than me, that is football. We disagreed. But Paul didn't tackle me, so I was okay out there!"
Derby may have lost, but they were cheered off by their fans who appreciated the effort put in by a side riddled with injuries.
Steven Bywater pulled out only minutes from the start with a shoulder injury, Stephen Pearson is in hospital with a suspected dislocated shoulder and substitute Robert Earnshaw pulled a calf muscle, leaving Derby with only 10 fit men for the final 15 minutes.
Jewell added: "There's not much justice in the game, particularly after battling so hard in the second half. I was bitterly disappointed with the first-half display, we looked frightened, scared of Liverpool.
"I couldn't wait to get at them at half-time, only 1-0 down. But in the second half we showed fight, and that is what the supporters want to see.
"We showed plenty of that in the second half, maybe we could have nicked it. I know they have also hit the bar, but Giles Barnes had a great chance for us.
"We ended up losing the game, but the supporters cheered them off because they had given everything.
"If Barnes' effort had gone in, we would certainly not have lost the match. But everything conspired against us. We lost our goalkeeper, Stephen Bywater, in the warm-up.
"Lewis Price had an excellent debut in goal, he was nervy early on but pulled off some fine saves.
"One of our own players takes out Pearson, who has ended up in hospital with a suspected dislocated shoulder. while Earnshaw damages a calf and spent the rest of the match as a passenger, we really only had 10 men out there.
"We were hanging on, and when you are playing one of the best teams in Europe you need everyone you can find."