The Dane was pitched off the road on lap 32 by a suspected left rear track rod failure when the car was under load in the fast right-hander at Turn 8.
Magnussen climbed out of the car unaided, but damage to the barriers led to a red flag. He was taken to the medical centre, but he was passed fit and soon returned to the paddock.
Brake temperatures are always on the limit in Mexico, and in Magnussen's case, they got too high as he was defending hard from Logan Sargeant, and winding the bias to the rear.
The American got past just a few corners before the crash, at which point Magnussen was told by his engineer that he had to get brake temperatures under control.
After the impact, TV pictures showed a brake fire starting around the left rear of the wrecked Haas.
During the red-flag period, the team checked the sister car of Nico Hulkenberg, but no signs of any problem were found, and the German was able to complete the second part of the race.
"It was a heat issue which caused a suspension failure," Steiner told Autosport. "It was heat from the brakes.
"Kevin was defending, and it tipped over. It was just because of the high temperatures here. We just need to manage it better. Nico's car was OK."
Despite the extensive damage and the loss of a complete set of the recent upgrade package, Steiner says that the team has enough parts for the rest of the season.
"We are okay. It's not ideal, but it's okay. It's always better at the end of the season. Now you can't any more parts even if you want them."
Seconds before the crash Magnussen was heard telling the team that "the rear left has completely gone here," and he suggested that he may have had a warning that something was amiss.
"I'm feeling okay," he said. "The suspension gave up. The rear left specifically lost a lot of grip a couple of laps before that, I suddenly lost a lot of grip on that, and then it gave up after.
"I think it was going alright. At the beginning of the race, it was better, and then suddenly I fell off more than the others. And then the suspension gave up.
"So I don't know if it's related. Maybe there's something there, but I need to go and talk to the guys."
Magnussen was seen shaking his hands after the crash as he had picked up an injury, but he insisted that he was okay: "I just got a knock on my hands, and they hurt a little bit, but they're fine."
