Sinner overcame a shaky start to claim a 2-6, 6-2, 6-1, 6-2 victory over American Mackenzie McDonald and reach the second round of the final Grand Slam of the year.
The Australian Open champion has been under intense scrutiny at the event after the International Tennis Integrity Agency (ITIA) said he tested positive twice for an anabolic agent in March.
Sinner has denied any wrongdoing and has continued to play after successfully challenging provisional suspensions.
"The response from fans, I feel it has been great, also throughout when the news came out, in the practice sessions, there was a lot of support, which I'm very glad and happy about," Sinner told reporters.
"It is still a little bit, you know, not easy. You have to go day by day... I was curious to see how the reaction of the fans has been, but it has been very positive.
"I was very glad how the support was, also playing against an American, it's a little bit different."
Following the ITIA's announcement, a number of players called out what they said were double standards in the sport, suggesting the Italian had received preferential treatment.
Fifth seed Daniil Medvedev said he found anti-doping rules to be a bit vague and hoped regulations are applied consistently for all players.
"I saw Taylor (Fritz) and I really like what he said. He said, 'It's only him (Sinner) who knows what happened exactly, so we can't know,'" Medvedev said.
"Nobody can know the exact truth except him, his team and maybe the independent tribunal."
However, Medvedev pointed out that when players are unaware how a banned substance entered their body they are provisionally suspended even if innocent.
Sinner was cleared of fault or negligence after a tribunal accepted his explanation he had inadvertently been contaminated with a banned substance by his physio.
"... So he knew what happened, and good for him, he managed to defend himself," the Russian said of Sinner.
"When you don't know, you get suspended. That's a little bit the tricky part, but that's how doping rules are."
Sinner, who takes on American Alex Michelsen in the second round, said he could not control what players think about the episode.
"There are some reactions. I cannot really control what they think and what they talk. That's how everything went and how it was, I already talked (about it)," Sinner added.
"I cannot control the players' reaction. If I have something to say to someone, I go there privately because I'm this kind of person. But overall, it has been not bad. I'm happy about that."
