The Lady Black Cats beat Reading 3-0 to make the semi-finals with Arsenal, Manchester City and holders Chelsea.
"If you want to win a trophy you've got to beat the best," Williams told BBC Newcastle ahead of Tuesday's draw.
"Whoever we get, we'll prepare appropriately. We're not going down without a fight."
Carlton Fairweather's side had drawn 1-1 with Reading in Women's Super League One on 26 March.
Ex-Doncaster defender Williams continued: "We played Reading in the league last week and we felt that we underperformed quite badly.
"So we had a chat first thing on Monday morning, we had a look through the videos, discussed what we needed to improve on and we applied that."
Sunderland Ladies have only played in an FA Cup final once, losing 2-1 to Arsenal in 2009.
"It would be massive if we get there [the final]," the 25-year old added. "It's every kid's dream, isn't it? You don't get many chances to play at Wembley and you've got to work hard to get there."
Defender Victoria Williams says Sunderland Ladies will "not go down without a fight" after reaching the last four of the Women's FA Cup.