Pep Guardiola told Chelsea co-owner Todd Boehly to back under-fire boss Graham Potter after Manchester City thrashed the Blues 4-0 in the FA Cup third round on Sunday.
Potter's troubled side were beaten by City for the second time in four days as their hopes of winning a domestic cup this season came to a painful end.
Already knocked out of the League Cup by City in November and defeated 1-0 by the Premier League champions on Thursday, Chelsea's turbulent season was pushed deeper into crisis as Guardiola's men ran riot at the Etihad Stadium.
Riyad Mahrez started the demolition with a fine free-kick before Julian Alvarez's penalty and a Phil Foden strike made it 3-0 before half-time.
Mahrez's late spot-kick capped Chelsea's first FA Cup third round exit since 1998 after they had finished runners-up in the competition for the last three years.
With Chelsea languishing in 10th place in the Premier League -- 10 points adrift of the top four -- Potter is already beginning to feel the heat just four months after replacing the sacked Thomas Tuchel.
The former Brighton manager will hardly have been comforted by the sound of Chelsea fans chanting Tuchel's name and sarcastically shouting "shoot" whenever they embarked on a rare attack during their latest abject defeat.
Chelsea have won only three of their last 12 games in all competitions, but Guardiola came to Potter's aid as he urged the Blues hierarchy to give him time to make his methods work.
"I would say to Todd Boehly, give him time. I know in big clubs, results are important but I'd say give him time," Guardiola said.
"What he's done at Brighton is outstanding, but we need time in the first season. I had (Lionel) Messi in Barcelona my first season so I didn't need two seasons because Messi was there."
- 'We are suffering' -
Chelsea did not muster a single shot in a first half even Potter described as "painful".
Potter could point to an injury crisis which kept nine players sidelined and led to teenager Bashir Humphreys making his senior debut in defence.
But the 47-year-old conceded performances must improve quickly.
"The results in a small space of time are not positive. You can make excuses and look for reasons or say it isn't good enough. Both of those answers are correct," Potter said.
"We have to keep improving and stick together because clearly we are suffering as a football club and it's not nice at all. But that's where we are at the moment.
"We can't do anything apart from do our jobs better and work harder. You understand the supporters' frustration, we respect that. But our job is to do our job and keep working."
Insisting he still has the backing of his players, Potter added: "I think there is support in the dressing room.
"We are just going through a bad moment. We have to stick together and keep working."
Meanwhile, the Football Association will investigate alleged incidents of homophobic chanting by City fans.
"We strongly condemn the use of the term 'rent boy' and we are determined to drive it out of our game," an FA spokesperson said.
"We continue to work closely with the Crown Prosecution Service, as well as the UK Football Policing Unit, in relation to the use of this term."