The Tigers claimed the three points thanks to strikes from Jake Livermore and David Meyler and an own goal from Martin Skrtel, while Steven Gerrard scored for the Reds.
The defeat leaves Liverpool seven points behind Arsenal at the top of the Premier League and Rodgers was upset at the errors his side made at the KC Stadium.
He told Sky Sports: "I thought that we had plenty of effort and commitment which I always get from the team but we just made too many mistakes today.
"Defensively as a team we made too many mistakes and obviously with the ball I don't think we created enough so it was a very, very disappointing result all round.
"We arrived into here our confidence and belief high. We didn't pass the ball well, we gave it away very quickly and we found ourselves a goal behind which was disappointing.
"We had plenty of possession but there was no real penetration with the team and that's something that we'll obviously look to put right for Wednesday (against Norwich)."
Liverpool were without striker Daniel Sturridge - who is out for six to eight weeks with an ankle injury - and Rodgers admitted they missed the frontman.
"There is no doubt that when you don't have a player of that quality, then it affects your team and we don't have a big enough squad to cope with a few players missing and that will always be the case.
"(If we've) got two or three of our players that are regulars in our team missing then we're a different team."