The Northern Irishman's side coughed up a three-goal lead to draw 3-3 at Crystal Palace on Monday, making Manchester City heavy favourites to claim the title.
Rodgers, whose team are a point clear at the top but have played a game more than City, said Liverpool would keep fighting until they finish the season against Newcastle on Sunday, despite conceding the title race was over after the Palace draw.
"The players have been incredible and they have allowed the supporters to dream," he said.
"To be the club that is top of the league by one point with one week to go, and you never know what might happen, has taken a huge effort.
"The only thing I will promise is that while I am here we'll fight for our lives. Our season doesn't finish until after Newcastle."
Liverpool's strong season means Rodgers is expected to agree to a contract extension which will keep him at the club until 2018.
Speaking at Liverpool's awards night on Tuesday, the 41-year-old thanked the club's owners for their belief in him.
"I would like to thank the owners and the executive team for what they have done for me since I have been here," Rodgers said.
"They brought a young manager of 39 into one of the biggest clubs in the world and gave me the chance to develop the vision of football that I have.
"If it wasn't for their faith in me I probably wouldn't be here given the pressures of modern football."
Luis Suarez picked up Liverpool's Player of the Year, Supporters' Player of the Year and Goal of the Season at the awards.
Captain Steven Gerrard said the Uruguayan striker was by far the best player he had ever called a team-mate.
"He's out there by a bit of a distance as well and that's no disrespect to all the players I've played with," Gerrard said.
"I've been lucky and blessed to been able to play with some top, top talents for both club and country but this fellow can do the lot.
"He's different than most footballers, his heart's as big as anyone's out there and I don't have to mention his talent. This is a fighter, a winner who doesn't give up.
"There's a little bit of disappointment looming around at the moment but I think if this fellow stays around for a few more years I think there's some really, really big nights to come."
