The 21-year-old, who scored 3 goals in 40 appearances for City, joined Southampton last week for an undisclosed fee, believed to be around £1m.
"It is my own fault," he said. "I was given a few chances in the first team but I did not make the most of them.
"There were a lot of experienced players ahead of me, but I have no-one to blame but myself.
"I would have been playing reserve-team football next season, so the Championship is a step up."
City boss Stuart Pearce defended his decision to sell a developing youngster who has shown lots of potential but admitted he 'hopes BWP will come back to him'.
"It wasn't a case of having to let one go, but at 21, Bradley needs to be playing first-team football - whether that was going out on loan, staying with us or, in this case, an offer coming in for him that I deemed good enough to accept," said Pearce.
"He did fairly well for us and is a decent player. He had his opportunity last season, started a couple of games and made more than 30 appearances for us.
"At the end of the day, we have got to back our judgement. He is a good lad, a decent player and will be successful professionally. At what level, though, I don't know yet.
"I've had to make a decision on everything I've seen, but I hope he comes back to haunt me."
In terms of recruiting, the latest player linked with a move to City is Peruvian defender Juan Vargas, who plays in Argentina.