Jeremy Wray was ousted by the club's majority shareholder, Betfair co-founder Andrew Black, and replaced by Sir William Patey.
Wray had been in charge for 18 months, but the club are under a Football League tribunal for spending more than 65 per cent of their turnover on players.
"It is important for me to have a team around me that I can trust," said Di Canio, speaking to the Swindon Advertiser.
"Jeremy Wray and Russell Backhouse, Phil Spencer and myself have worked tirelessly as a team to bring success to this club but now with Jeremy going and Russell potentially soon to depart, half of that team may soon be taken away, and, as much as I have loyalty to Swindon and its fans, I also have loyalty to Jeremy and Russell and these events have certainly changed the dynamics."
Di Canio suggested Backhouse, a director, would resign from the board in protest.
Wray, who opted to leave Swindon's board entirely after being deposed as chairman, suggested he had been dismissed due to a clash with Black.
"I have spoken to Sir William and he is a gentleman, an extremely able man and a thoroughly likeable guy. I have no doubts he will do a very good job as chairman. The decision certainly caught me off guard. I was told 10 days ago. Some people leave when it's going well, they get out at the top and some get sacked when things are going badly, but you don't often get chucked out when things are going well," he said
"There have been personal issues. Andrew Black has his reasons and I respect his decision as majority shareholder. He can put who he likes in charge and I just felt it wasn't appropriate for me to remain on the board."