Chelsea's dispiriting performance away at the Etihad Stadium also prompted the travelling fans to chant in support of former manager Thomas Tuchel, who was sacked in September last year, and the club's former owner Roman Abramovich.
"We can't do anything apart from doing our jobs better and working harder. We understand the supporters' frustration. That is understandable and we'll respect that," Tuchel said.
"Our job is to keep working, see the situation for what it is. Of course there are always other opinions, negativity and criticism because the results haven't been positive. That's part of the job and the challenge."
Chelsea's next game is a Premier League London derby away at Fulham on Thursday. Potter's side are 10th in the league, 10 points away from a top-four spot.
"We need to stay together as group, support each other, and I'm sure we will get the support of the supporters when we see good performances and results."
Potter laments Chelsea’s ‘painful’ FA Cup defeat as pressure mounts
Image: Alex Livesey/Getty Images
Chelsea boss Graham Potter said Sunday's 4-0 FA Cup loss to Manchester City was "painful" and he understood the supporters' reaction as the London side suffered a sixth loss in nine games to pile on more misery in the Englishman's short tenure.
Chelsea were booed at halftime when they went into the break 3-0 down before they lost to City for a third time in as many months this season.
The defeat marked the first time in 25 years Chelsea had exited the FA Cup in the third round, while they are also out of the League Cup after losing to City in November.
"I thought we were second best to a very good side. Obviously, we're not in a great moment," Potter told reporters.
"Manchester City did really well in terms of stopping us, but at the same time we struggled.
"We had to chase the ball against Man City and we were caught between trying to commit more men forward and not being opened up. The first half was painful and tough for us all.
"Congratulations Man City. They deserved to win of course. We're disappointed because we've gone out."
Chelsea's dispiriting performance away at the Etihad Stadium also prompted the travelling fans to chant in support of former manager Thomas Tuchel, who was sacked in September last year, and the club's former owner Roman Abramovich.
"We can't do anything apart from doing our jobs better and working harder. We understand the supporters' frustration. That is understandable and we'll respect that," Tuchel said.
"Our job is to keep working, see the situation for what it is. Of course there are always other opinions, negativity and criticism because the results haven't been positive. That's part of the job and the challenge."
Chelsea's next game is a Premier League London derby away at Fulham on Thursday. Potter's side are 10th in the league, 10 points away from a top-four spot.
"We need to stay together as group, support each other, and I'm sure we will get the support of the supporters when we see good performances and results."
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