Mayer said he was fired via a text from one of Ben Sulayem's assistants on Tuesday.
"For a federation that relies on volunteers to fire by text somebody who has made a significant contribution does not speak well of the management of the federation," Mayer said.
He said the reason for his dismissal as a steward was Ben Sulayem "took offence" at the contents of an appeal document filed by the Circuit of the Americas (Cota), host of the US Grand Prix in Austin, Texas.
Mayer represented the Austin organisers in a 'right of review' hearing into a decision to fine them 500,000 euros, with 350,000 euros of it suspended, after a track invasion at the end of the F1 race on 20 October.
Cota officials were "not best pleased" at the judgement, Mayer said. A similar situation at the Canadian Grand Prix this year led to a warning.
Mayer, who was acting in the appeal in his role as sporting organiser of the three grands prix in the USA, said that his involvement in the appeal initially led to to him being removed from the stewards panel at the Sao Paulo Grand Prix earlier this month, before his firing as a 2025 steward this week.
"The official reason that will be given is they felt there was a conflict of interest with the FIA as I had led the right of review in my role as organiser," Mayer said.
"But that is not why I was fired. Being an organiser is a role that I have fulfilled, benefiting the FIA, for over 12 years. This isn't new.
"In spite of the matter being resolved quietly and amicably, he's still upset and decided to fire me. After 15 years of volunteering my time as a steward, a decade teaching other stewards and hundreds of hours volunteering in other roles, I got a text from one of his assistants."
Mayer said that Ben Sulayem felt an element in the right of review paperwork "was a personal attack on him".
"I didn't write that part of the document, but it was my job to present it," Mayer said.
"There was no intention of trying to cause a problem with the FIA and I will continue as the sporting organiser of the three US Grands Prix. This was such a minor point that it is baffling that anyone would take such offence."
Cota succeeded in having the language of the right of review verdict changed, removing a finding that organisers had "failed to take reasonable measures".
"In US legalese, that is synonymous with negligence, which is problematic for a US corporate body," Mayer said.
"Following the right of review hearing, the stewards subsequently agreed with us and changed the penalty to a breach of Article 26.7 of the F1 regulations, which states that no one is allowed in the track before all the cars are in the pits, which is a statement of fact. Some fans did reach the track.
"In the process, there were hurt feelings on behalf of the president, which I think is odd because there was no cause for his feelings to be hurt when everyone else dealt with this in a professional manner."