Magnussen qualified seventh for Haas on Saturday, and ran as high as fifth in the opening stages before slipping behind Red Bull’s Sergio Perez and Mercedes’ George Russell.
But when Perez and team-mate Max Verstappen both retired in the closing stages due to a fuel pump issue, Magnussen rose to fifth place once again, giving Haas its best result since the 2018 Austrian Grand Prix.
It was the first time Haas had finished in the points since the 2020 Eifel Grand Prix, ending two difficult seasons that have seen the team struggle for performance and fail to finish a race any higher than ninth.
Asked how he would understand Haas’s result in Bahrain, team principal Steiner said: “I don't want to understand it, I want to live the dream!
“[Kevin] knew that he had a good car. We saw that [in qualifying]. But then you still need to deliver.
“The longest stint we did up to now was 18 laps in a row. So now to do 57 was quite an achievement, and we didn’t put our foot wrong, nothing - the team didn't do anything wrong. Everything was well prepared.
“Also the qualifying, you are fighting on a difficult position, but everybody did their job and made the right decisions at the right time. So it was a very good weekend.”
Magnussen’s points haul put Haas third in the constructors’ championship after the opening race, only trailing Ferrari and Mercedes, who locked out the top four positions.
“I don't think that will stay for long,” Steiner said. “But anyway, we’ll enjoy the dream.”
Haas opted against developing its car at all for the 2021 season, preferring to place full focus on the new technical regulations arriving in 2022. The decision meant last year was a transition season for the team in which it failed to score any points.
Steiner said Magnussen’s fifth-place finish ranked among one of Haas’s most important results since the team joined the F1 grid in 2016.
“The last two years, we had to get by - now we are back,” Steiner said.
“So for sure it’s special, because everybody had lost the trust in a very short period of time. I mean in '18, to finish fifth and feel good, then in '19 with the bad car, people lost completely the trust. [They said] the team is for sale, the team is whatever. We're still here and we are back now.”
Steiner expressed confidence that Magnussen’s charge to fifth would not be the only chance Haas had to fight for points this year, believing it could carry its good form into the rest of the season.
“Alfa Romeo is very strong as well, so I don't take it easy now that we are where we are,” Steiner said.
“We need to work out and keep on improving the car. Also, with upgrades later on in the year. That is what we are doing.
“But I'm pretty sure that we’ll keep on scoring points.”
