The McLaren driver, who had finished on the podium in his first Formula 1 race in Australia, made contact with the right rear tyre of Kimi Raikkonen's Ferrari during the opening lap.
As a result of the incident, Raikkonen got a puncture and Magnussen was forced to pit to replace his front wing.
The rookie was also given a five-second stop-and-go penalty for the crash, and has been given two penalty points on his licence.
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Magnussen went on to finish in ninth position.
"I'm sorry for the team that I messed it up in the first corner," said Magnussen. "I think we could have got some good points today so I'm really disappointed with myself that I did that mistake.
"That stuff happens. You just have to learn from it, I guess. The car was really good and I'm sorry for the team that I did a mistake."
The Dane, in only his second Formula 1 race, said his lack of experience was no excuse for his mistake.
"No excuses. I'm not happy. When you make mistakes is not nice. I take the blame for the bad position that we got.
"Formula 1 races are long and I shouldn't have made a mistake like that in the first corner.
"We could have had a lot more points today. Not much to say. I'm sorry for the team."
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