Haas is to voice its "annoyance" to the FIA regarding the black-flag furore that played a part in wrecking Kevin Magnussen's last race in Canada.
Magnussen was involved in a lap-one incident with Lewis Hamilton that damaged his front wing but which appeared to have little effect as the Dane maintained his starting position of fifth.
Following behind, Alpine's Esteban Ocon, knowing the FIA would be listening in on the radio messages, communicated to his team the front-wing endplate was "hanging on" and that it would 'hit him in the face' if it dislodged.
Soon after, the FIA black flagged Magnussen, forcing him to replace the wing, albeit without consulting with Haas as to their position on the matter.
"I share the annoyance [with Magnussen] that we were not even consulted, that we didn't get a call saying 'Hey guys, your front wing, you've a piece flapping off. What is your opinion about it?' because we know how it is designed," said Steiner.
"I cannot sit here now and say it would never have fallen off but it wouldn't have done because there is zylon on top it and zylon doesn't break.
"We need to respect the race director, but my personal disappointment, and I have to actually ask Peter Crolla, our team manager, to go and bring this up.
"We should have at least had a call asking for our opinion rather than just getting a flag, and that's it. Over and out.
"We would have changed the wing anyway because we lost downforce but at a more convenient time. Just a lap later we would have maybe lost 10 seconds less because it was under a virtual safety car.
"It was a little disappointing, and it came over because another driver cried on the radio, that he was scared for his life, so it was reactive. Are we back to that?
"We would have said 'Don't worry for the next 10 laps, we will change it when we get into the pits, but at the moment it's not falling off'.
"But we never got that call, and you cannot debate that because it is too late."
Asked whether Crolla would speak to the FIA ahead of this weekend's British Grand Prix, Steiner added: "It will be brought up.
"Pete will bring it up with the race director and say 'Next time, it would be nice if you ask us because we've an opinion about it as well'."