The opposition became too difficult against the Polish Iga Swiatek, ranked 9th.
The match lasted for one hour and 17 minutes.
Still, Peterson was not too disappointed after the match.
She is rock hard focused on improving her weaknesses and learning from every match.
- I feel that if I can go up a few levels in a few moments, it will make a big difference, she says to TT.
"I want to beat them"
- I think it has been a very good test for me to know where I stand, so that it becomes extremely clear to me and my coach what I need to improve, she continues and says that the last time she met Iga Swiatek, it felt afterwards that she needed to get better at "pretty much everything".
It did not feel that way this time.
- For me, it's not just about going out and meeting them and thinking it's fun, but I want to beat them, I really have faith that I can do it, says Peterson about the highly ranked opponents she has met recently.
With tonight's loss, Peterson is knocked out of the tournament's singles section, but she is expected to line up in the women's doubles later.
It was not unexpected that the Swede, who is ranked 92nd, would be beaten by Iga Swiatek.
But there were certainly no shortage of surprises in the ladies' second round of the grand slam tournament.
That French Alize Cornet, ranked number 61, would beat third-ranked Spaniard Garbine Muguruza in two straight sets with the numbers 6-3, 6-3 was unpredictable.
Cheers gave confidence
The big bang was still the Danish talent Clara Tauson - the 19-year-old is seen as one of women's tennis' greatest talents and is predicted a brilliant career.
She beat sixth-ranked Anett Kontaveit from Estonia with the numbers 6-2, 6-4.
Tauson itself is ranked number 39.
- I felt so good out there and I could hear several cheers which gave me good self-confidence, and I played a very good match, said a happy Tauson after the one hour and 19 minute long match to the news agency AP