Osaka triumphed 6-2 6-4 on Saturday in a final that was overshadowed by a dispute between opponent Serena Williams and umpire Carlos Ramos.
Williams was issued a code violation for what the official deemed to be coaching from Patrick Mouratoglou, irritating the 23-time major champion who insisted she was not a cheat.
A point penalty for racquet abuse led to her branding Ramos a "liar" and a "thief" and she was then docked a game, after which the American called for the match referee and alleged she was being treated differently to male players.
Williams, who has since been fined $17,000 for her conduct, was in tears in the closing stages, while Osaka - Japan's first grand slam singles champion - was also visibly emotional after a dramatic final in New York.
But, as the dust settled on Sunday, Osaka began to appreciate the magnitude of her achievement, as well as focusing on future ambitions.
"Everyone wants to win slams and be number one, so that's my goal too," she told Omnisport.
"It still doesn't really feel that real. Right now what I'm feeling is very tired. That's the main thing I feel.
"Hopefully as that wears off I'll start feeling more happy."
2 weeks of flawless tennis.
2 weeks of steadfastness.
2 weeks of composure.
— US Open Tennis (@usopen) September 8, 2018
Asked whether the incidents involving Williams and Ramos altered how she felt about the victory, Osaka added: "I'm not really sure what happened between Serena and the umpire and I keep getting asked questions about it, but I'm not too sure.
"For me I think it's still a win, so I'm just going to count it as that."
Getty Images. Caption:US Open champion Naomi Osaka.