Pegula was demolished 6-2, 6-3 by the world number 116 in just 58 minutes on Court Two.
It was a bitter blow for 2024 US Open finalist Pegula, who has never been past the quarter-finals at the All England Club.
The 31-year-old played with heavy strapping on her right knee and never looked comfortable in a lacklustre performance.
"She played incredible tennis. Do I think I played the best match ever? No. But I wasn't that bad. It was just her day today," Pegula said.
"I think I could have served better but I was having trouble with the conditions. It was very humid and the court was slow.
"I tried my best to match her level and I thought I would close the gap in the second set. But she didn't drop her level at all. She was forcing a lot of my errors."
Since losing last year's US Open final against Aryna Sabalenka, world number three Pegula has been eliminated before the quarter-finals in all three of her Grand Slam appearances.
"It's probably the worst result I've had all year. I haven't lost in the first round of a Slam for a long time. That sucks," she said.
"I feel like I'm playing as well as I was at the end of last year. But it's hard to put it all together over two weeks. Sometimes it doesn't align.
"I'm managing the knee and I have a bit of a neck injury as well. But I feel good overall. That's why it's disappointing.
"The most frustrating thing was I wasn't able to figure it out, which I feel I should be able to. "
It was only Cocciaretto's second win against a top-10 player.
The 24-year-old has never been past the third round at Wimbledon, and her best Grand Slam performance was a run to the last 16 at last year's French Open.