Bruce was axed by the Black Cats in November and replaced by Martin O'Neill after a disappointing start to the campaign.
The former Wigan and Birmingham chief admits he was disappointed not to be given more time at the Stadium of Light and he has backed O'Neill to be a success on Wearside.
"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.
"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."
Bruce added: "We finished tenth last year which was a decent finish for them and we made many, many changes and 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.
"You have to accept it. If you are going to be in the Premier League and manage there you have to accept unfortunately things like that have happened.
"It's difficult, but you just dust yourself down and go again.
"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.
"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."