One judge scored the bout 115-113 for Pacquiao, while two others saw it 115-113 for Bradley, even though it appeared Pacquiao hurt Bradley throughout the fight - particularly with his straight left hand.
Pacquiao fell to 54-4-2 with 38 wins inside the distance, suffering his first defeat since 2005.
Bradley improved to 29-0 with 12 wins inside the distance.
Judge Jerry Roth (115-113) awarded the fight to Pacquiao while CJ Ross (115-113) and Duane Ford (115-113) gave it to the American, but the crowd responded with boos after 12 rounds which the Filipino had appeared to dominate.
"I accept what the result is," Pacquiao said ringside. "I respect the judges, I cannot blame them. It is a part of the game. I give thanks to the Lord. I do my best but my best wasn't good enough."
Asked if he thought he had won the fight, Pacquiao replied: "Absolutely, yes," and the crowd erupted with cheers.
"It was a good, competitive fight," said Bradley. "Every round was pretty close. Pacquiao won some of the early rounds. I controlled the later rounds with my jab. I need to go home and review the tape."
"He is a strong puncher. He rocked me a couple of times in the fight but I held my ground and fought to the end. This is boxing," he said.
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