Goals from Damien Delaney and Dwight Gayle in the final 11 minutes saw the table-toppers squander a three-goal lead to draw 3-3, making Manchester City strong favourites to claim the title.
|15/2||Liverpool are 15/2 with Paddy Power to win the title this season|
"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."
Speaking at Liverpool's awards night on Tuesday, Rodgers thanked the club's owners for their belief in him amid reports he is in line for a new contract.
"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."