The Reds won their way through to the fourth round of the EFL Cup with family commanding 3-0 victory over the Rams at iPro Stadium.
Goals from Ragnar Klavan (first for the club), Philippe Coutinho and Divock Origi gave Liverpool their comfortable win but Klopp feels his players could have produced even more as he continues to strive to get the absolute best out of his squad.
"We were better and deserved to win, we created chances," said the German.
"Could we have done better? Yes, a lot.
"Is it important tonight? No, because that's what you want to have.
"You need to be 100 per cent professional, be really serious and take games like these like they are. They could be difficult but it wasn't difficult because of us.
"The opponent was ready for each opportunity but we didn't give them [any]. So it was good. First half, we could have been a little bit better in the last pass. Second half, we could have been better in the counter-attack. That would have changed the result a little bit but we scored the goals, so it's not that I would say 'I would rather score this goal than this goal'.
"I take them like they are, 3-0, all good."