The New Year's Eve loss at Anfield, decided by Georginio Wijnaldum's early header, left City 10 points adrift of leaders Chelsea in third place
Manchester City manager Pep Guardiola acknowledged his team face a battle just to secure a top-four Premier League finish following their 1-0 defeat at Liverpool.
The New Year's Eve loss at Anfield, decided by Georginio Wijnaldum's early header, left City 10 points adrift of leaders Chelsea in third place.
They will slip out of the Champions League places altogether if Arsenal and Tottenham Hotspur win on Sunday against Crystal Palace and Watford respectively.
Asked if City face a battle to hold onto their place in the top four, Guardiola replied: "Definitely. It will be very difficult for all the teams."
With Chelsea registering a record-equalling 13th successive victory against Stoke City, Guardiola conceded it was difficult to envisage his side reeling the west London club in.
He even went as far as to suggest that City could switch their priorities to the Champions League and the FA Cup if a title tilt appears beyond them.
"They've won 12 or 13 games in a row so it's true that dropping points is not easy," Guardiola told reporters.
"But we start the second leg (of the season), so with all due respect for the other teams, we have to focus on ourselves and try to do what we have to do to win the games.
"When you are 10 points behind, you have to be focused on just the next game. We cannot talk about this kind of goal.
"You just focus on the next game, which starts the day after tomorrow, the second leg.
"There are many, many things to fight (for): the Premier League, the Champions League, the FA Cup, the Champions next season.
"When it's finished, with one month or two months left, we're going to see what is our position and in that moment we're going to decide what our target is."
City are next in action on Monday, when they welcome Burnley to the Etihad Stadium, while Liverpool will go in search of a fifth successive league victory at third-bottom Sunderland.
Liverpool's win took them back to within six points of Chelsea and manager Jurgen Klopp's words suggested his side are relishing their role as leaders of the chasing pack.
"We cannot have a look at Chelsea," he said.
"Obviously they are unbelievably strong. They're on an outstanding run. They won now 13 games already. Not bad!
"But can you imagine how annoying it is when you win 13 games in a row and there's still one team only six points behind? But I'm sure they don't think about this, so why should we?
"It is completely not important, what happens in this moment, apart from that we win games.
"That's the only thing we are really interested in and it's so difficult in this league. It's unbelievably difficult."
Liverpool struck from their first incursion into City territory, Adam Lallana crossing from the left and Wijnaldum meeting the ball with a thumping header that ripped past Claudio Bravo.
City, who recalled Sergio Aguero after suspension, upped their game in the second period after David Silva was moved into a central position, but failed to create a single clear-cut chance.
The hosts lost captain Jordan Henderson to a heel problem midway through the second period, with Divock Origi taking his place.
Klopp said the injury did not affect the same heel that caused Henderson problems last season, but his assessment of the issue was downbeat.
"In this moment there's a little bit of pain in the heel," Klopp said.
"If Hendo is limping there's probably a little bit more pain (than there would be for another player). We have to see. I don't know exactly in this moment."