Jakupovic was leading the match after claiming the first set 6-4 and the second set looking like it was heading for a tiebreak. The game had been going for one hour and 52 minutes when she fell to the ground.
"On the warm-up at 9 o'clock, I was having chest pain," Jakupovic said.
"In the match, after 25 minutes or so, I was getting difficulty, like an asthma attack, which I don't have.
"So I called the physio on the court and I was getting better. After some time, the end of the second set, the physio came again, I thought I would be better.
"The points were getting bigger and I couldn't breathe out on the court. I couldn't stand up."
The Slovenian put the onus on Australian Open officials, saying the conditions weren't right for matches to go ahead.
"I think it was not fair because it's not healthy for us," she said.
"I was surprised. I thought we would not be playing today but we really don't have much choice.
"If they don't put us on the court, maybe we get fined - I don't know.
"It would be maybe better to see if tomorrow is better. They still have time."
"It was really bad. I never experienced something like this and I was really scared. I was scared that I would collapse. That's why I went on the floor. Because I couldn't walk any more. When I was on the ground it was easier to get some air."
As Jakupovic was being treated by medical staff, former Australian Open semi-finalist Eugenie Bouchard called for the doctor after winning the second set and was taken off the court to be treated.
Bouchard was able to make it back out onto the court for a deciding third set, but shortly after the match got back underway her opponent, Xiaodi You, called for the trainer.
Mandy Minella, the world No. 140 from Luxembourg, tweeted her shock at qualifying being allowed to take place, despite the City of Melbourne Council advising locals to "stay indoors, keep windows and doors shut, and keep pets inside".
As qualifying got underway, Serena Williams' coach Patrick Mouratoglou tweeted it was "not the best air quality this morning in Melbourne".
Tournament organisers have technology on the ground to assess the air quality to help guide them as to whether conditions are too dangerous for players.
