Graham Potter said he "hasn't done enough at Chelsea to have too much good faith" as pressure mounts on his position after Sunday's 2-0 defeat at Tottenham Hotspur.
Second-half goals from Oliver Skipp and Harry Kane condemned Chelsea to their ninth Premier League defeat of the season, leaving them 14 points off the top four.
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Sources have told ESPN that the club's owners, led by Todd Boehly and Clearlake Capital, remain supportive of Potter but are mindful of growing unrest within the club's fanbase.
That resolve could be tested as the possibility of qualifying for next season's Champions League continues to recede but Potter cited the difficult spells Mikel Arteta and Jurgen Klopp endured at Arsenal and Liverpool respectively as examples the club should follow.
"There's always that question [over the owner's loyalty], absolutely," Potter said. "You can't stop that question while the results are like there are and I accept it. It is part of the job. We were talking before the game about watching [the Amazon documentary] All or Nothing and Arsenal. Two years into Mikel's reign he's close to getting the sack, people wanted him out and it is a disaster.
"Obviously now, things have changed a little bit. That's just the way it is. Look at Jurgen's situation. He doesn't get results and all of a sudden people want him out. That's just the nature of football. I haven't done enough at this club to have too much good faith and I also accept that as well.
"My job is not to worry too much about that. I understand the question and where it comes from. I just try to focus on the team, keep supporting the players because I really like these players. They are good lads, they want to do better, they want to win but at the moment we are suffering. That's my responsibility."