The 23-time grand slam champion was given a coaching violation and a point penalty for smashing a racquet in the second set, while her remonstrations with umpire Carlos Ramos resulted in the 37-year-old being docked a game.
Williams called Ramos "a thief" and finished the match in tears as Osaka claimed her first Major in a 6-2 6-4 triumph over her idol.
After a long wait in which both players showed their emotions, jeers greeted the start of the trophy presentation, with the American comforting Osaka.
While Williams, seemingly still fuming with the officiating, would not entertain questions, she asked the crowd to congratulate the 20-year-old champion.
"I don't want to be rude, but I don't want to do questions," Williams said, fighting back the tears. "I just want to tell you guys: [Osaka] played well and this is her first grand slam.
"I know you guys were here rooting and I was rooting, too, but let's make this the best moment we can and we'll get through it.
"Let's give everyone credit where credit's due. Let's not boo any more. We're going to get through this. Let's be positive. Congratulations, Naomi. No more booing.
"Thank you to my team, thank you crowd, you're the best in the world. Thank you so much."
Clearly feeling let down by the way the final played out, Williams appeared to suggest it could affect her future participation at Flushing Meadows.
"I really hope to continue to go and play here again," she said, adding with a smile: "We'll see. It's been tough here for me but thank you so much."