The 20-year-old replaced Darius Vassell with 22 minutes remaining and slammed home City's fourth goal within a minute of coming on.
"Usually I'm coming on with 88 minutes gone, and it's frustrating," he told the City website.
"I was happy because we were battering them, and I thought, 'I could get on here'."
He did, and much to the pleasure of the home crowd.
Asked if he is aware of his popularity among City fans, he answered: "Sometimes, but that's probably because of my brother! I think Shaun being here before has a lot to do with all that."
A humble Bradley also accepted Stuart Pearce's decision not to start him with Andy Cole suspended.
Antoine Sibierski scored his first goal of the season, won man-of-the-match, and nodded down Trevor Sinclair's cross for Wright-Phillips to score.
"It was between me and Antoine, but you can see why the gaffer played him," added the City youngster.
"Right from the beginning he's got a header in down to Vassell, and he got in from it. He's got real quality in the air."