The Spaniard's car slammed into the track wall at 200 mph after colliding with Esteban Gutierrez's machine before barrel rolling twice.
The wreckage landed upside down on the gravel -- but Alonso emerged unscathed.
"I am lucky to be here and thankful to be here. It was a scary moment and a scary crash," said the 34-year-old.
"When I stopped, I saw a little space to get out of the car and I went out quickly just to make sure that my mum, who was watching the race on TV at home, could see that I was OK."
Writing on Twitter, he said he was "aware that today I spent some of the luck remaining in life." He also posted an Instagram photograph of him reading a newspaper headlined: "Luckiest man alive."
Alonso said of the incident: "You are just flying and then you see the sky, the ground, the sky, the ground.
"I didn't know where I was because I was so far from the track. You want to stop, and it doesn't stop. It keeps going and going and going."
Gutierrez, who was also unhurt, hugged Alonso at the side of the track before both men were taken for medical assessment.
Speaking on Monday, Alonso's teammate Jenson Button said he believed the controversial halo device, designed to shield a driver's head from debris and due to be brought in next season, would have helped.
Critics of the halo say it would take longer to get drivers out of the cockpit after a crash.
But Button said: "There was no need for him to get out [of the car] in that situation.
"There's more safety risk of things hitting our head than anything happening when the car's upside down."