Bruce was sacked at the end of November after two and a half years in charge following a poor start to the season in which Sunderland won just two of their opening 13 matches.
"It is never easy when you get the sack, especially when it's a public sacking of course," Bruce told Sky Sports News. "It is unfortunate the way it went and I am disappointed we didn't get a bit longer, but all managers are going to say that I suppose. We finished 10th last year, which was a decent finish for them and we made many, many changes."
He added: "With changes you need time, and unfortunately it didn't go our way and the crowd got impatient and we know the way football is, that is the disappointing thing.
"But you have to accept it. If you are going to be in the Premier League and manage there you have to accept that unfortunately things like that happen.
"It's difficult, but you just dust yourself down and go again."
Taking advantage of his enforced break from the game, Bruce was in Dubai watching the first day of England's first Test with Pakistan.
Assessing his future, he added: "I am just going to recharge the batteries and see what comes up and have a break from it and see what appears on the horizon."
Since Bruce's departure, new manager Martin O'Neill has turned the club around as Sunderland have taken 13 points from seven matches, which is of no surprise to the former Wigan and Birmingham boss.
"Frustration is there because I knew the nucleus of the side was decent, we just didn't have that bit of luck that is needed," said Bruce. "They are a good squad of players, decent lads, and Martin has inherited a decent squad. Martin has done remarkably well, which I knew he would do, and I wish them well."