Rodgers admitted the crown would go to Liverpool's north-west rivals after the 3-3 draw at Crystal Palace on Monday night, but told his press conference for Sunday's meeting with Newcastle that he had not given up on a first league trophy in 24 years.
Firstly, the Reds must beat the Magpies at Anfield and hope West Ham overturn leaders City at the Etihad Stadium on Sunday afternoon, with both matches live on Sky Sports.
Rodgers is hopeful that the Hammers have enough quality to help Liverpool out with their side of the bargain and said: "It's certainly not over.
"First and foremost, we can only concentrate on our job, our job is to win the game.
"I think Alan (Pardew) will come and he'll want to finish his season strong. We know that it's a tough game.
"But the combination of us at home and our supporters has been fantastic for us. To look to get 16 wins out of 19 come the weekend would pencil in a great return for us at home.
"For them (Manchester City), West Ham have got some really talented players. To be able to go to Tottenham and win 3-0, you can certainly go to Manchester City and win, specially if you a guy like big Andy (Carroll) up front with the quality that he has.
"City have got a really good defensive record, 14-odd clean sheets I think, so it shows that they're a really difficult team to play against.
"So our focus is on ourselves, if we do our job then I'll be happy."
Rodgers will soon enter the final 12 months of the three-year deal he signed in June 2012 when taking over from Kenny Daglish and he said a new contract had all but been agreed.
He said: "I've obviously been in discussions with the club and there is the framework of a deal that is in place.
"But I have always said it will be at the end of the season.
"I want nothing to detract from what has been a great season for ourselves. Hopefully we will resolve it over the course of the off-season."
The Northern Irishman went on to insist that even if the club finish as runners-up in the Premier League, they would have exceeded expectations.
He added: "Firstly, I'd want to congratulate my players on the season. I think we've had a remarkable season, the players have put Liverpool on the world map again in terms of what we're looking to achieve here as a club.
"The performance level has been exceptional over the season and come this Sunday we'll fight to the very end.
"If we win the game and end up not winning the title I think to finish second to the richest team in the history of sport really shows the measure and the progress we've made here.
"What is poignant is that you guys, the media, are talking about us for the title. It's a huge compliment to what we're doing here, to be considered for it.
"I think for us this is only the beginning. I've been here two years and we've been progressing, this year we've made a step.
"I see and hear about all the teams that are going to improve and I think we'll improve dramatically ourselves next season.
"We've got young players who have been through a great experience which will only bode them well for the future.
"And players like Steven Gerrard, at 33 years of age, this is his first example of this type of run-in. He will be better next year also.
"So, for us, it's only just the beginning. We're really looking forward to finishing this season strongly.
"Tick the box at the weekend, it'll be a tough game and then be prepared and really excited about next season."