City have been English champions in six of the past seven seasons under Guardiola - Liverpool won on the other occasion - but the gap between them and the table-topping Reds has prompted some pundits to write off their title chances after their latest loss.
"I don't see there's any way back for Manchester City now," former Liverpool defender Jamie Carragher said on Sky Sports.
"Sometimes you need to lose so people realise what you've done - but this season Manchester City will not win the Premier League."
Former City defender Micah Richards added: "I wouldn't say it's the end of an era.
"It's a difficult time, but they're going to find a way to get back. Some of the players have let Guardiola down today. They're a shadow of their best."
Yet with 25 games and 75 points still to play for, Guardiola refused to concede the title despite the 11-point gap between City and Liverpool.
"Teams are good and we can't handle it right now," he admitted. "I have to find a solution to be solid. What can I say?
"These players have given me the chance to live maybe the best years of my life. All I can do is be here to try to find a solution."
In what is being regarded as comments directed towards his playing squad and the club's future ambitions, Guardiola added: "In the right moment the club will take a decision about what is needed to allow this club to still be there."