Haas has been fined a total of €10,000 (AU$16,540; £8,660) following a breach of the tyre regulations.
Due to first practice at the Hungaroring being declared wet, it meant an additional set of Pirelli's intermediate tyres were made available to all drivers who had used the green-striped rubber during that session.
Under article 30.5g of the FIA's sporting regulations, a used set of intermediates must then be both physically and electronically returned prior to the start of qualifying.
However, whilst Haas physically returned the used set, they did not do so electronically, leading to a fine of €5,000 per car.
In qualifying, Haas endured the high of Hulkenberg reaching Q3, with the German starting 10th, whilst Magnussen was dumped out of Q1 and will line up 19th. The Dane finished just over six-tenths of a second behind his team-mate.
A naturally frustrated Magnussen said: “Just a disappointing qualifying for me. I just can't seem to find the confidence in the car on one lap – on long runs and high fuel in the race it's a different story.
“Seeing what's in the car, Nico doing Q3, it's, of course, disappointing not to be able to extract that myself. I feel more confident in the race but then again we as a team have a limitation there too. We'll just try again (in the race) and see if we can pull something out of the hat.”
In contrast, Hulkenberg obviously declared himself “happy”, although claims he “didn't have any more pace” in Q3 to finish any higher than 10th.
The Hungarian Grand Prix starts at 1500 local time (2300 AEST; 1400 BST).