The 36-year-old has run the League Two club since 2011, and is one of only seven female chief execs across the Premier League and English Football League.
Radford's husband is the club chairman, but people treat her differently in board meetings.
"My points are equally valid," she told the BBC.
"When you walk into a room and someone's like, 'oh, you look gorgeous today' ... I don't think they'd say that to another man."
Speaking to BBC Radio 5 live, Radford admitted that she has had to learn to let remarks go "over her head".
She said: "I just think, 'OK, it's their problem, not mine'. But equally, is it preventing other women from getting involved in the sport, in the fact that I'm not standing up and saying actively: 'No, this isn't good enough'?"
"If I go into a boardroom, a lot of the time I'll be talking to other chairmen of other football clubs or other executives at a high level and they'll choose to just smile if I say anything, and talk to my husband."
"Then we'll be coming home in the car and I think, 'What is this about? Why is our sport so full of dinosaurs?'"
Radford thinks that social media campaigns empowering women to speak out about harrassment and abuse, such as #MeToo, have made a difference.
"People are calling it out and saying it's not acceptable," she said.
"Beforehand I would just duck my head down and accept the abuse whereas now I'm actually saying: 'I'm not going to patronised by you, I'm equally able to do a good job.'"