The 61-year-old was sacked from the Stadium of Light post on Saturday evening, hours after the Wearsiders' 1-0 home defeat to Manchester United.
O'Neill told Radio 5 Live: "I am still pretty disappointed, frustrated as much as anything else but life goes on.
"I'm in the business now where I think very little shocks you about professional football especially in the last 10 years. You can lose a job in management if your tie doesn't fit your suit.
"With the experience I have had over the years...also coming into the football club at a time when the club was pretty well on its knees. I believe I saved it from relegation last year and I thought that opportunity should still have been afforded to me."
The former Leicester and Wycombe boss also reiterated his belief that Sunderland did not have enough quality through the team.
"The DNA of Sunderland Football Club is about passion - it has been throughout the years and that is very important, very important to the supporters of the football club.
"It carries you a certain distance (but) of course you have to have ability to play.
"Overall we've got some very fine players at Sunderland at this moment.
"But we haven't enough true ability throughout the side to be able to cope with every single thing that is thrown at us.
"I don't think it is a major criticism, it is there for all to see, it's actually a fact.
"It's something you have to try and cure and want to rectify as soon as possible - that is not always possible given the time."