Bent has joined Villa in a deal that will see them pay Sunderland an initial £18million, but add-ons could see the total fee rise by another £6million.
Bruce said: “It’s hugely disappointing that Darren has decided that his future lies away from Sunderland and the players, our supporters and the club as a whole have every right to feel massively let down.
“The timing is especially hard to take, given that we are progressing positively and are in a great position to push on.
“Everyone has been nothing but supportive of Darren in his time at Sunderland but it’s obvious he’s not been himself in training and we’ve certainly not seen the best of him in games in recent weeks – and we now understand why.
“I’ve always stated that my aim is to build a talented, young squad for the long-term to help the club achieve sustained success and I want Sunderland fans to know that our ambitions haven’t changed on that front.”
Sunderland chairman Niall Quinn added: “Darren has now left the club and it’s important we move on quickly.
“We’ve worked hard in the last 36 hours to get what we feel is a fair price for him. Of course it presents us with significant challenges from a football perspective which we didn’t envisage, but we’ll deal with it and are working hard to find a solution both in the short-term and more importantly the longer term.”
