Di Canio was dismissed after just 13 games in charge following the 3-0 defeat at West Brom last month, amid suggestions some of the club's senior players had been instrumental in his removal.
But, in a statement, the Italian described the reports as "wholly untrue" - and repeated his belief that he was capable of turning the club's poor start to the season around.
Di Canio said: "There was no training ground bust-up as some are reporting and many of the players have since sent me messages thanking me for my time as their manager and helping them improve as footballers.
"We could see that results had not gone as well as any of us had hoped, but I felt as a team we could turn things around."
Di Canio was widely credited with keeping Sunderland in the Premier League last season after replacing Martin O'Neill at the end of March.
He became an instant hero after inspiring a famous 3-0 win over north-east rivals Newcastle at St James's Park in only his second game in charge.
But despite bringing in 14 new players over the summer, his side took just a single point from their first five games of the new season.
Di Canio said: "When you bring in 14 new players, many from overseas and very few with Premiership experience it is going to take time for them to adapt to the English game and to gel as a team.
"As I have said many times, I love English football and I feel that my time at the club has been unfairly cut short as given the chance, I am certain that had I been allowed longer, I would have been able to develop the team to achieve the success Sunderland fans desire."
Saturday October 512:45 Manchester City v Everton 15:00 Cardiff City v Newcastle United 15:00 Fulham v Stoke City 15:00 Hull City v Aston Villa 15:00 Liverpool v Crystal Palace 17:30 Sunderland v Man Utd Sunday October 613:30 Norwich City v Chelsea 13:30 Southampton v Swansea City 16:00 Tottenham v West Ham United 16:00 West Brom v Arsenal WHO DO YOU WANT AS MANAGER? PLEASE VOTE: