Jake Livermore's deflected shot gave Hull the lead before Liverpool skipper Steven Gerrard scored from a free-kick to make it 1-1 at the break.
But David Meyler gave the home side the lead again and Martin Skrtel put through his own net to give Steve Bruce's side their first ever win against the Merseysiders.
"In the main, our form has been very good so I can't criticise the players too much," said Rodgers.
"If there's anyone to blame, blame me as manager. Ultimately it is down to the manager.
"The players have been brilliant over the course of the season, we just had an off day.
"We made mistakes with the goals but we go into two home games and that is what we will focus on."
Rodgers also confirmed he might look to strengthen his squad in the January transfer window, especially with striker Daniel Sturridge ruled out for up to eight weeks with an ankle injury.
"I think every window for us will be exactly the same. If there is a player that we think can improve our squad, I am sure we will be able to go out and get that player," he added.
"We have a few injuries to key players that leaves us light but it's probably no different to a lot of squads.
"But we have other players that are working very hard and they will get an opportunity now.
"The responsibility now falls on everyone to keep up the performance level."
The problem was that LFC dominated possession... in their own half. Gerrard having to start play from the edge of his own penalty area is nonsense. Henderson just runs around like a headless chicken and hasn't got a clue what he is doing (with or without the ball). Lucas can't pass and can't tackle. Suarez nevers looks when he passes so it's almost random whether or not he plays a good ball. Sterling shouldn't even be on the pitch and he knows it. But the most frustrating thing of all is the number of goals LFC have conceded by fart-arsing about with the ball in their own half because they are clearly under orders, on pain of death it seems, never to hoof the ball up field or into touch even when surrounded by 5 opposing players. Aaarrgghhh!!!- quozzbat