Boehly only arrived at Stamford Bridge in the summer, replacing Roman Abramovich, and brought in Potter from Brighton in September, who lasted less than seven months.
Potter succeeded Thomas Tuchel and Boehly was previously adamant that he would stick with Potter despite mounting pressure over his future.
Chelsea have had a horrendous season and following a 2-0 home defeat to Aston Villa on Saturday, the west London club are 11th in the Premier League table.
They have won just three games in 2023 despite spending over £600m on players since the summer.
Carragher hit out at the American as he posted on Twitter along with two laughing emojis: ‘Todd said he would be different to Roman.
‘I feel for Graham Potter, but it was inevitable. You don’t change Tuchel for Potter. Ridiculous decision to start with.’
Jamie O’Hara, speaking on Sunday prior to the news of Potter’s sacking, said that the Englishman was struggling to manage ‘big personalities’ in the squad.
‘Chelsea are 11th – for me, it’s unacceptable,’ he told Sky Sports. ‘The amount of money they’ve spent, [co-owner] Todd Boehly has come in.
‘I know you’ve invested in Graham Potter. You had to get him away from Brighton, but he’s miles off it. The players are not responding to his tactics.
‘The teams he picks from the start are strange. He’s constantly changing it. Then the subs he makes in the second half are all over the place.
‘I don’t think these players are having Graham Potter. What I’m seeing from this side and the players that are there, I think he’s struggling with big characters.
‘He’s not used to having big characters at Brighton, Graham Potter.’