The Slovenian world number 180 had to be helped off court after she retired at 6-5 5-6 against Swiss Stefanie Vogele in the first round in Melbourne.
“It was really bad. I never experienced something like this,” Jakupovic said.
“I was really scared I would collapse because I couldn’t walk any more.”
Qualifying was delayed by an hour on Tuesday and practice was temporarily suspended because of the air quality.
Organisers said the conditions were expected to improve and would be “monitored constantly”.
Asked about the decision to continue with qualifying, Jakupovic said: “I think it was not fair because it’s not healthy for us.
“I was surprised. I thought we would not be playing today but we really don’t have much choice.”
People in Melbourne were advised to stay indoors and keep pets inside on Tuesday.
At least 28 people have died and an estimated 10 million hectares (100,000 sq km) of land has burned since 1 July.
Jakupovic added: “I’m angry and sad. I’m more sad because I had the win [in my grasp] and I just couldn’t finish it.
“I don’t have asthma even and I don’t have breathing problems from the heat. I was scared.”
Australian Open organisers said prior to Jakupovic’s retirement: “Further decisions will be made based on onsite data, and in close consultation with our medical team, the Bureau of Meteorology and scientists from EPA Victoria.
“As always the health and safety of our players, our staff and our fans is our priority.”
Eugenie Bouchard also left the court during her qualifying match against You Xiaodi, complaining of a sore chest. The Canadian returned after a medical timeout and won 4-6 7-6 6-1.
Meanwhile, Maria Sharapova’s exhibition match in Kooyong, which is in the east of the city, was called off after both players complained about the air quality.
The Russian was trailing Germany’s Laura Siegemund 7-6 5-5 when the match was ended.
“I started feeling a cough coming toward the end of the second set but I’ve been sick for a few weeks so I thought that had something to do with it,” Sharapova told broadcasters after the match.
“But then I heard Laura speak to the umpire and she said she was struggling with it as well.
“We were out there for over two hours, so from a health standpoint it’s the right call from officials.”