The 63-year-old was jettisoned after less than six months in charge at Goodison Park after a short meeting with majority shareholder Farhad Moshiri on Wednesday.
The former England manager was brought in as Ronald Koeman's replacement in November but his rudimentary style of play proved deeply unpopular with fans of the Merseyside club and the atmosphere became toxic.
But Allardyce was unhappy with the way his exit was touted in the media well before he had received official confirmation.
"I'm surprised how it came about. It seemed to be done and dusted through the media before I met Farhad," he told talkSPORT radio.
"I think it was out there in the open for a couple of days. That leaves you with the certainty of what was going to happen.
"It was slightly disappointing. Who was involved in that I couldn't tell you, but something as delicate as that is something you want to be confidential."
Allardyce said most of the club's fans were behind him as he lifted the club away from relegation danger to finish a comfortable ninth in the Premier League.
"I think there were certainly more Everton fans who were happy with what we were doing and going in the right direction than the ones that weren't," he said.
"Those who show discontent are the ones who are more open and vocal about it. The ones who are satisfied don't really say too much."
Former Watford and Hull City manager Marco Silva is the favourite to take over and could complete the move to Goodison Park six months after the club failed to prise him away from Vicarage Road.
Everton moved quickly to clear the decks following Allardyce's sacking, with his backroom staff of Sammy Lee, Craig Shakespeare and Martyn Margetson released and director of football Steve Walsh replaced by PSV Eindhoven's Marcel Brands.
The Dutchman has been tasked with an overhaul of the system at the club, having first been contacted by the Toffees two years ago prior to Walsh's appointment.