“We were better tonight and we deserved to win, we created plenty of chances. Could we have done better? Yes, but is that important? No,” Klopp said.
“You need to be 100 percent professional in games like this, which could be difficult, but we were ready for every opportunity.
“We could’ve been better in the first half with the last pass and in the second with our counter attack but we will take 3-0 all day.
“The pleasing thing is it’s not we are surprised by it. I have always thought the difference between home and away shouldn’t be that big when you’re a good side, which we are.
“That’s what we expect from us. Tonight was very professional from us.
“This is a very important tournament for us, for the players, and we have to show it from the first second. Let’s go for it.”
Klopp became embroiled in a heated discussion with the fourth official after seeing Coutinho be on the end of a number of hefty challenges, but the German played down the confrontation.
“It is so close when someone flies in three or four times like they did, and I said to the fourth official ‘Please tell him’,” said Klopp.
“He didn’t hit the player, I saw that, but it was so close. But that’s my problem how I reacted and nothing happened.”
Derby manager Nigel Pearson, whose side are struggling for goals and are 20th in the Championship, admits they could not cope with the quality of their Premier League visitors.
“I would be first to accept there is a gulf in class tonight, and where we are and where we aspire to be is a considerable difference,” he said.
“For us to progress as a club we need to build a squad which can compete anywhere.
“All of the goals had an element of we could have done better, so that is frustrating. Mistakes cost you dearly against sides like this.
“After that it is damage limitation to make sure it is not an embarrassment.”