Sunday's 3-1 loss at the KC Stadium - the first to the Tigers in the Merseyside club's history - was disappointing not only because of the result but also in terms of performance.
With nine-goal striker Daniel Sturridge injured and playmaker Philippe Coutinho only fit enough for a place on the bench, the Reds struggled to pose much of a threat while also looking far from comfortable at the back.
Rodgers stressed he is the one who should ultimately be held accountable but has said there need to be greater contributions across the squad.
"It was painful, that was the overriding feeling," he said.
"Probably more the performance disappointed us because when you perform how we did we didn't deserve to get anything from it.
"In the main our form has been very good so I can't criticise the players too much and if there was anyone to blame, blame me as the manager.
"When we lose a game we all get criticised but the criticism has to come to the manager, I am responsible because I pick the team.
"I will always demand the best. We are not here to be great losers, we are here to win.
"The responsibility falls on everyone to keep up our performance level."
Having scored seven in their last two matches Liverpool managed just nine shots, only four of which were on target, despite dominating possession against Steve Bruce's side.
Raheem Sterling and on-loan Chelsea forward Victor Moses were the players charged with filling the boots of Sturridge and Coutinho but both failed to deliver.
"I thought both players worked hard in the game," he added.
"Raheem is still only 18, he has been in and out this season but is still a fantastic talent.
"Victor is a player who has great ability and it's been a bit difficult for him because he's not had a run in the team but he is still an important player for us."
Fortunately for Rodgers, Coutinho has been declared fit - Sturridge will be out until mid-January with a sprained ankle - for Wednesday's home game against Norwich but even so the manager still expects more from others.
"Coutinho allows you to penetrate - I think that was one of the things that was missing from our performance yesterday," added the Reds boss.
"We were too slow and too predictable then when he came onto the pitch, people started to run beyond and get forward because he plays the forward pass.
"Of course, we're a better team whenever we have both (Sturridge and Luis Suarez) at the top of their game.
"But like we have done in the past, we'll find different ways to win.
"We're not going to succeed if we can only rely on those two and we can't rely on one player (Suarez) - it has to be about the team and that's what we'll focus on.
"The responsibility is for the people coming in and for the rest of the team.
"We have to find a different way of getting the result."
Sturridge has been sidelined with his third injury inside six months - he previously sprained an ankle on England duty in June before being hampered by a thigh problem.
Rodgers insists, however, that the 24-year-old has just been unlucky with his latest knock.
"It probably surprised us how serious it was but the scans don't lie," he said.
"It's just really unfortunate. When you're that level of player, the idea is to be fit every day and to play in every game and I think he has shown that when he plays, his goal record is fantastic.
"We just hope he can get back quickly. He recovers very well. We'll soldier on with what we have and the players, I know, will give absolutely everything."
Sturridge's injury and an unimpressive first few months for summer signing Iago Aspas, who has only just returned from a torn thigh muscle, may force Rodgers' hand when the January transfer window reopens.
"I think every window for us will be exactly the same - if there's a player we think can improve our squad and in particular the team, I'm sure we will be able to go out and get that player," he said.
"It was always going to be the case that if we had a few injuries to key players, that leaves us light.
"It's no different to a lot of squads, but for us it's even more prominent because Daniel Sturridge and young Coutinho were not playing and they are good players."