Daniel Agger's header from a corner and Luis Suarez's 20th of the season from a free-kick put paid to the Tigers and while the performance was far from the Reds' best, it was significant after back-to-back defeats at fellow top-four rivals Manchester City and Chelsea.
"I said to the players afterwards that I thought that was our best win of the season," said Rodgers.
"In a lot of games we've been vibrant with great energy, scored goals and performed well, as well as won.
"But on the back of the games that we've had over this period - and to play with a lot of the same players against a team that won their last Barclays Premier League game 6-0 - we knew we were going to have to tough it out today and dig in.
"We might not have always been at our best, but we got two great goals, had other opportunities and actually restricted Hull to no shots on target.
"I'm very, very pleased with today because it was a great victory for us."
Suarez's free-kick meant he became the joint-fastest player in Premier League history to reach 20 goals, achieving the feat in 15 games. Andy Cole also got to 20 on New Year's Day 1994 while with Newcastle.
"Today was very much about the team. Luis will, of course, always get the plaudits because he's a world-class player," added the Reds boss.
"Nine out of 10 players would not have played today. He had a real bad knock on the top of his foot from the Chelsea game.
"I know, having managed and worked with players, that most players wouldn't have played with what he had today.
"He had strapping on it and he put himself out there for the team yet again. That's why he gets the goals that he does, because he's so determined.
"But it was very much a team effort today. It was a great header from Daniel Agger from the corner and that set us off."
Hull boss Steve Bruce felt the packed festive programme finally caught up with his side.
"Towards the end we were game enough to keep trying but you could see a lot of tired bodies and the third game in six days was a bit too much for us," he said.
"It was a big ask for us, we needed to be right at it and be fresh and it was a bit too much for us.
"A footballer can play a match every day but he can't play with the same intensity.
"We looked tired towards the end, your concentration goes and you don't have the energy to compete.
"Sometimes you have to say you were beaten by the better team and we were today.
"The disappointing thing is the game was settled by two set-pieces. Luis Suarez's free-kick has made the game comfortable for them in the end."