The Indian food group axed Allardyce within a month of completing their takeover of the club, with Steve Kean currently in temporary charge as a long-term replacement is sought.
"If this is the way the club's going to be run from now on, I don't want to be part of it and I want to leave," said the 26-year-old in remarks reported by the Sun.
"As captain it's very difficult to say this but I've thought long and hard about it. Nobody in football understands the decision to sack Sam.
"We could have been relegated last year and Sam saved the club, so how can he be treated like this now?"
Samba exempted chairman John Williams from blame, though, before pleading for a swift decision over Allardyce's replacement.
"I'm sure Mr Williams would not have made this decision. He's a football man and respects what a great job Sam has done," he said.
He added: "The players and fans need answers about the club's future. Unless we commit to who the manager is, how can we attract big players in January?"
Source: PA
Source: PA