Goals from Jake Livermore and David Meyler, as well as a woeful own goal from Martin Skrtel, earned the hosts a much-needed three points.
Mistakes throughout the game from the Slovakian defender and his partner Kolo Toure helped the Tigers on their way to a memorable first league victory over the Reds, and Rodgers admitted his side had not displayed the quality they have for much of the season at the KC Stadium.
Asked if he was disappointed by the performance, Rodgers replied: "That’s an understatement, it was very disappointing. We’ve made too many mistakes today, with and without the ball; we never created enough and never kept the ball for long enough.
"I always felt we were in control of the game, but we needed to show a bit more quality. In our last two games we’ve conceded six goals and we need to be much better than that."
Shortly before kick-off, it was confirmed that Daniel Sturridge would be out of action for up to eight weeks, but Rodgers believes injuries will give fringe players an opportunity to prove themselves.
"Daniel could be out for up to eight weeks, which is a big blow for us, and Philippe [Coutinho] never trained all week; he’s had some injections to even get on the bench today," Rodgers said.
"You take those two out and they’re obviously two very, very good players who have been very efficient for us this season, but this little period now will test us and we’ve got players that’ll come in and it’ll be a good opportunity for them.
"I’ve not had much chance to speak with him, but I’ve no doubt he’ll be disappointed as this is a very busy period we’re coming into, we’re a squad that needs as many as its good players as possible."
Rodgers also revealed that Toure had picked up a knock against Hull ahead of a run of six games, including trips to Tottenham, Manchester City and Chelsea, in December.