Pacquiao sealed a unanimous points victory to regain the belt, having lost it to Bradley in a highly controversial split decision 22 months ago.
The American, who was undefeated prior to the bout, connected with the chin of the 35-year-old in the ninth, but it was not enough to secure the knockout he promised.
He told reporters: "I tried. I really tried. I wanted that knockout. Manny's a great fighter, maybe one of the best ever. I lost to one of the best."
Pacquiao's win has since re-fuelled speculation over a potential fight with Floyd Mayweather.