Potter was appointed to replace Thomas Tuchel at the start of the season following his superb three-year spell at Brighton.
Chelsea initially impressed under Potter but results and performances soon fell away and the 47-year-old was sacked in April after less than seven months in the job.
Potter won just 12 of his 31 games in charge of the Blues, who had dropped into the bottom-half of the Premier League during his tenure.
Despite Chelsea’s poor form under Potter, Fabregas disagreed with his dismissal and has accused the Stamford Bridge owners of ‘panicking’.
‘I understand that the top, top teams nowadays panic very quickly,’ Fabregas – who spent five years at Chelsea – told The Athletic.
‘Like Chelsea, you are eighth and you make a change and now you are 14th. A panic change does not always guarantee you that you’ll get better.
‘Sometimes it does, sometimes not. But if you really believe – I believed in (former Chelsea manager Graham) Potter.
‘I know the results weren’t great but if you believe in him the way you say you believed in him… they had given him a five-year contract. Maybe give him some time. It’s proven with other coaches that it worked.’
Following Potter’s sacking, Chelsea appointed club legend Frank Lampard as caretaker manager until the end of the season – though the team continued to struggle, eventually finishing 12th.
Ex-Tottenham boss Pochettino was confirmed as Chelsea’s sixth permanent manager in five years after the final day of the season.
Discussing Pochettino’s arrival in west London, Fabregas added: ‘I’ve never worked with him, obviously I’ve heard of him. I’ve met him a couple of times on holiday in Ibiza.
‘I’ve played against him obviously when he was at Spurs and we’ve chatted after matches.
‘I think he seems like a very reasonable man, very calm, that gives a lot of confidence to younger players and has a good structure and has a staff that he trusts so much.
‘I hope he’s the right man to bring back Chelsea to the position where they belong.’
Chelsea have given Pochettino a two-year contract, with the option of a further year. The Argentine, who has also managed PSG and Southampton, begins the role at the start of July.
MORE : Andy Cole claims Chelsea star ‘wouldn’t improve’ Manchester United
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