Alonso had been running as high as seventh during the race, but hit trouble around lap 25, when he ran very deep under braking at Turn 1. He pitted immediately, but then overshot his markers as his brakes failed, causing his McLaren pit crew to take evasive action.
"I had no brakes - I think the rear disc stopped working," Alonso said immediately after the race.
"My pit stop was a scary moment - I didn't have much rear braking for my whole in-lap, then even less at the stop. It was scary for the mechanics, but luckily it didn't hurt anyone."
Alonso's team mate Jenson Button also struggled during what was a miserable race for McLaren, with the Briton describing the handling of his MP4-30 as "pretty scary".
"As soon as I touched the throttle, it just snapped away from me," Button reported. "It was unpredictable: in low-speed corners, the car was just slow, because I got wheel-spin immediately; in the high-speed stuff, it was just scary, because the rear end would snap away immediately under power.
"I was talking to my engineers for most of the race to try to find out what the root of the problem was, and we switched on quite a lot of handling balance changes to try to cure it. It got a little bit better towards the end of the afternoon, but it was a pretty tough afternoon."
McLaren have now failed to score points in the first five races of 2015 - their worst ever start to a Formula One campaign.