The Briton missed out after a yellow flag warning meant he had to slow on his final attempt to get out of the bottom five.
"Everyone did their second laps and I didn't," Norris told Sky Sports television. "It was unlucky, that's all. I had to lift.
"There's a long race ahead, we have some good tyres in the bank, I'm still hopeful we can get a good result. I think the car is quick. Bit frustrating, but nothing I can do."
It was the Briton's first elimination at the first hurdle since Las Vegas last November when he started 16th and then retired in the race.
Norris is second in the championship but 62 points behind Red Bull's Max Verstappen.
The run-up to the race weekend has been dominated by talk of potential team orders at McLaren and Norris being helped by Australian teammate Oscar Piastri, who went through to the second phase.
