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."