Taylor, 26, made her debut keeping wicket for Northern Districts in the West End Premier Cricket Competition against Port Adelaide Magpies.
The two-day event is the highest level of cricket played in South Australia outside first-class cricket.
"I am completely proud of what I have achieved today," Taylor told the BBC World Service's Sportsworld programme.
"I would like to think I am not going to be the last woman to play in men's A grade.
"To be the first was never a plan of mine, it has just happened that way. I have to thank the Jets for letting me have that chance.
"It was a long day, it was tough, but overall I was pretty happy with my performance."
Former Australia Test cricketers Darren Lehmann, who is the current coach of the men's national team, and Ryan Harris have previously represented Northern Districts in the West End Premier Cricket Competition.
The second day of the two-day match will be next Saturday, when Taylor will bat.
"It has been a rollercoaster for me and them these past few days, but the guys were brilliant about it," she added.
"There was pressure internally, rather than worrying about external factors, but I am happy with what I have done."
Taylor, who has played in men's league cricket in England, is also playing 50-over state cricket for South Australia in the Women's National Cricket League, and will feature for Adelaide Strikers in the inaugural Women's Big Bash League, a Twenty20 competition.
"One day there might be a girl who comes through and doesn't want to play women's cricket, and wants to see how far she can go in the men's game," said Taylor.
"For me personally, it was just to make a me a better women's player."
Earlier this year, England seam bowler Kate Cross became the first woman to play in the 123-year-old Central Lancashire League.
England's Sarah Taylor made history on Saturday by becoming the first woman to play Australian first-grade cricket.