The fall occurred in the third set of Sinner's 4-6, 6-3, 6-7(6), 6-2, 6-3 win, with the 24-year-old briefly clutching at his left hip afterwards, but he soldiered on to seal the win for a meeting with Nuno Borges in the second round.
Sinner, who injured his elbow during the fourth round of his triumphant Wimbledon run last year, was thankful that his latest tumble did not cause any lasting damage and highlighted the need to continue moving positively.
"One fall is a tough one because you can get injured," Sinner told reporters.
"It's the most normal thing. Grass courts are like this. Especially the first couple of matches when the grass is very new, you slip a bit more.
"I got lucky there because things can go wrong very quickly. I try to still trust in my movement. Also the third, fourth and fifth sets were very important to keep moving in a natural way, which I did. I'm very glad nothing happened."
The Italian said being a talented skier in his youth did not necessarily mean that he had better technique to avoid injuries during falls.
"There are some movements you can't really control. It's just normal instinct," Sinner said.
"Skiing can help you in certain moments, but not when you fall, when you have zero control. We did a lot of prevention before this tournament because we knew things like this could happen potentially.
"Today it happened. So the most important thing is to take this part away and keep moving like before because if not, when you're very scared, everything goes too slow. On this surface, you can't do that."