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After the damaging 3-3 draw at Crystal Palace Rodgers suggested that the championship was destined for Manchester City.
The Reds are still top of the league but Manuel Pellegrini's side are only a point behind, with two matches still to play and a superior goal difference.
Kenny Dalglish brought Suárez to Anfield in 2011
But speaking to a captive audience at the club's inaugural awards night, the Reds boss suggested there was still a glimmer of hope ahead of Sunday's match against Newcastle.
"This season the players have allowed the supporters to dream and for a club of this size and magnitude - to be a point ahead at the top of the table with a week to go, you never know what can happen - it has been magnificent," he said.
"I promise for the time I am here we will fight for our lives and we won't finish until Newcastle."
Brendan Rodgers and Ian Ayre were present at the awards ceremony
Rodgers, who received a standing ovation from his players after winning an outstanding achievement award less than two years into his tenure, maintained there were still positives to take from the season.
He added: "Monday night was difficult. If you were in the changing room you would have felt how much it mattered to everyone.
"The key thing to remember is the journey we are on is going to have good and bad times but through it all we have to stick together as that is the Liverpool way.
"We will finish the season strong and keep going to strive to be the best."
Striker Luis Suárez, already a two-time player of the year after winning the Professional Footballers' Association and Football Writers' award, won the goal of the season, players' player of the year and player of the year, voted for by fans.
Noel Clark presented Raheem Sterling with his award
"He has thoroughly deserved it. As a team they have been outstanding but he has been absolutely phenomenal," added Rodgers.
"The great thing about Luis Suárez is his professionalism. To play the games he plays to the level he plays takes huge professionalism. I am delighted for him."
Captain Steven Gerrard believes Suárez is the man who will ensure a successful future for the club.
"Luis seems to be cleaning up at the moment, he's won everything, and we are lucky to have such a world-class talent like Luis playing here with us and helping us to great things and be successful," said the England captain.
"He is out there by a big distance (as the best player he has played with) and that is no disrespect to all the players I've played with, there has been some top talent for club and country, but this fella can do the lot, he is different to most footballers.
"I don't have to mention his talent, you can see it out there, and he is a winner who is doesn't give up.
"There is some disappointment looming around but if this fella stays around for a few more years I think there will be some really big nights."