The 36-year-old is coaching at a higher level than any other woman in European men's football following her move to the French Ligue 2 side earlier this month.
But, while the news has made headlines across the world, Costa asked to be regarded as just another coach.
"I know it's a big step," she said on Thursday. "I know because I had a career before in a men's world mainly. So I know it's an important day and it can open other doors, or not, but we are in 2014.
"I understand your surprise and the quantity of press and the impact it has had, but this should be a normal thing. Look at me as a normal coach."
Costa, who has coached in the lower reaches of Portuguese football and also scouted for Scottish Premiership side Celtic, admits that she has faced sexism but is in no doubt that she can prove her detractors wrong.
"I will not lie, yes I did (face sexism), but I'm here and I'm here by hard work," she said. "I'm not here for other things.
"But, yes, I faced some episodes; it's normal when you're a pioneer or when you start doing something that's not common for a woman, but that doesn't mean that you're not serious or you're not working there by your confidence or the work you've shown.
"If I am afraid or if I don't think I'm capable of this, I wouldn't be here."
Clermont finished 14th in the French second tier this season and Costa is eyeing a campaign of improvement.
"We have our objectives and we are professional," she added. "If a club doesn't have a huge budget, that doesn't mean that the players shouldn't be committed and ambitious for winning. Winning is a word that from now Clermont Foot will have."
