“I wasn’t really happy with my performance,” admitted the 23-time Grand Slam champion, who is playing in just her third tournament of 2019 having lost in the Australian Open quarter-finals before retiring in the second set of her third-round match against Garbine Muguruza with a viral illness at Indian Wells last week.
“Had to take a lot of time off the last week,” she said. “It’s definitely not easy at all. But I’m through it. That’s that. I’ve just got to get my game back to where I know it can be.
“I told myself at the end of the second set that I could not lose this match.
“I knew that I could play a lot, lot, lot better. I just had to be better. At this point it was irresponsible to be playing the way I was playing in the second set.”
Serena, an eight time winner in Miami, was just relieved to make it through to the third round where she will meet China’s Wang Qiang who thrashed Britain’s Jo Konta, the 2017 Miami Open champion, 6-4 6-0.
The former world number one was certainly rusty in her first ever match against the 63rd-ranked Swede, despite starting strongly and easing into a first set lead.
Peterson, however, who lost in the first round in Indian Wells, produced some excellent tennis in the second and managed to break down Serena’s serve to take the match into a deciding set.
As the South Florida sun began to lower, Serena appeared to struggle with her ball toss.
“It was interesting, because first of all it was dark out there, which was really odd,” Williams said. “I wasn’t sure if there should be lights. The shadow was so intense it was actually dark.
“Then there was light, but only on my side. That was weird because I literally couldn’t see.
“But I need to just move on and really focus on playing better or not being in the tournament much longer.”
Williams, 37, is still seeking a first title since the birth of daughter Alexis Olympia.
She admitted it was sometimes hard to stay patient, although she believes returning to the top 10 after her extended maternity leave qualifies as “extremely successful”.
“It’s just a step at a time,” she said. “Just because my level of success is so much higher than what’s natural, I have to take these moments and say, ‘You’re doing great,’ encourage myself in a positive way so I can get that success that I want to have since coming back from the baby.”
Meanwhile, after picking up her first career WTA Tour event win on Thursday, 15-year-old Cori Gauff fell to 14th-seeded Russian Daria Kasatkina 6-3 6-2 while 17-year-old Amanda Anisimova lost 6-3 1-6 6-4 to Estonian Anett Kontaveit.
Earlier on Friday, World No, 1 Naomi Osaka endured a rollercoaster start, advancing to the third round with a 6-0 6-7(3) 6-1 win over Belgian Yanina Wickmayer.
After facing eight-times Miami champion Serena in her first match last year, Osaka might have expected an easier opener against the 141st-ranked Belgian qualifier.
Yet that was not the case as she needed more than two hours to dispose of her Belgian opponent, having dispatched the 23-times grand slam singles champion 6-3 6-2 a year earlier.
“It was really hard for me, I think, emotionally in the second set because I just started thinking about winning, not exactly the things I could do in order to win,” said Osaka.