Speculation about Potter’s longevity at the club has run more rampant in recent days, but the Blues boss insisted he did not need validation from anyone outside the confines of his club.
"The owners are billionaires so they’re quite smart," he said. "Smarter than me, that’s for sure. So they understand the challenges that we have and the direction we want to go in. I’ve been here four months and five, six weeks of that have been lost to international football.
"I think Pep (Guardiola) was (at Manchester City) a year before they’d won anything, and then obviously Mikel (Arteta) and Jurgen (Klopp) took a bit of time. But obviously it’s maybe different for me, for some reason. But I don’t put a timescale on it. I know the responsibility we have here.
"But also I know that I am capable, and I know the quality that I have and I have the full support of certainly the owners, the players and the staff here. And you can see by the support we had (against City), it was fantastic, so there will always be people that doubt.
"There’s nothing you can do, but certainly I’m not here to convince anybody. I’m here to do my I work and then if that convinces then that’s fine."
Chelsea go head-to-head with City again on Sunday, this time at the Etihad in the FA Cup third round.
Raheem Sterling and Christian Pulisic were both forced off the pitch on Thursday, adding to an injury nightmare Potter summarised by saying: "I’ve never experienced anything like it."
The pair were still being assessed following the City defeat and could be added to a growing list of sidelined talent that already includes N’Golo Kante, Reece James, Wesley Fofana, Mason Mount, Ben Chilwell, Armando Broja, Ruben Loftus-Cheek and Edouard Mendy.
The Blues boss argued the fitness crisis, alongside a start to the season that paused for two postponements and the World Cup, did not seem like a particularly fair fragment of history on which to judge his early era at Stamford Bridge.
He said: "I don’t read the newspapers, I stay away from social media, I have no idea (what they are saying). I’ve had some support, I’m not naive to know that when you have the results that we have there’s not going to be criticism and negativity, that would be strange for me to think that.
And again, I’m not sitting here [as] some egomaniac that has all the answers and gets everything right. Of course that’s not the case. But like I said, at the same time, there’s some challenges that we face, there’s some margins in the Premier League that are difficult.
"We’ve had a massive transition, problems in terms of injuries don’t make it easy to be stable, but it’s sort of blah, blah, blah isn’t it? People want to see results, and ‘shut up Graham what are you talking about? We need to win’."
Additional reporting from PA