Hamilton was leading when he was called in for fresh tyres during a late safety car period, dropping him to third.
Mercedes F1 boss Toto Wolff said: "The answer is we got the maths wrong.
"That one goes on the team and I apologise. He's a great leader and a great driver. I am sure he will understand sometimes we make errors."
The mistake handed victory to Hamilton's team-mate Nico Rosberg and also cost Hamilton a position to Ferrari's Sebastian Vettel.
It cut the world champion's advantage in the championship over Rosberg to 10 points.
Hamilton was visibly distraught afterwards, but refused to blame the team for the error.
After crossing the finish line, Hamilton slowed to a stop at the Portier corner - which faces out to the Mediterranean Sea - seemingly to gather his thoughts.
