The Italian world No.1 also revealed at his pre-US Open news conference that, although he knew he was innocent, he was still worried about what the case's outcome would be until he discovered he wouldn't be suspended.
"It has been a very tough moment for me and my team," Sinner said at the site of the year's last grand slam, where he is the men's top seed.
"It still is."
Play begins on Monday at Flushing Meadows, where Sinner is scheduled to meet first-round opponent Mackie McDonald, an American ranked 140th, on Tuesday.
McDonald got into the main draw when Rafael Nadal withdrew earlier this month.
"It's not ideal," Sinner said with a bit of a chuckle when he was asked about the timing of this week's news of his doping case.
He also called the outcome "a relief."
The 23-year-old, who has Australian Darren Cahill s one of his two coaches, tuned up for the US Open by winning the hard-court Cincinnati Open on Monday.
The next day, the International Tennis Integrity Agency (ITIA) announced he had failed two drug tests in March — one during a tournament in Indian Wells and one eight days later — but ruled the banned steroid Clostebol entered his system unintentionally through a massage from his physiotherapist, Giacomo Naldi.
Sinner's defence was that his fitness trainer, Umberto Ferrara, purchased an over-the-counter spray that contained Clostebol in Italy, then gave it to Naldi, who used it on a cut finger. Sinner said Naldi then gave him a massage.
The player Sinner beat in the Cincinnati final, Frances Tiafoe, was also asked about the news.
"He's an incredible player, and (governing) bodies made a decision. They went and did that; he's cleared to play. That's pretty much what I have to say about it," Tiafoe said. "All the best to him in the US Open."
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