The Spaniard, who briefly led the race, was handed a five-second penalty for an incorrect starting position, which he served when team-mate Lance walk retired from the race on lap 18.
The 41-year-old took the podium to celebrate his third place behind the dominant race-winner Red Bulls Sergio Perez And Max Verstappen.
But he then almost immediately took a hit with the extra time penalty when race stewards decided he had not correctly executed the earlier penalty.
It turned out to be a sour end to the weekend after cheering scenes in the Aston Martin garage, but Alonso described his frustration.
“It doesn’t hurt much to be honest, I was on the podium, I did the photos, I held the trophy, I celebrated with the champagne but apparently I have three points less.
“I think the FIA has fallen short today, more than a disappointment on our part. You cannot apply a penalty 35 laps after the pit stop. They had enough time to inform us about the fine.
“Maybe if I knew I would be 11 seconds ahead of the car behind. Today we didn’t put on a good show for the fans.”
The result has been cancelled George Russell a third place after a strong weekend for the Brit, despite obvious problems with the W14.
Russell said: “I think the penalty for Fernando is quite heavy, they are the deserving podium finishers today, but I’m taking a trophy so I’m not complaining too much!”