Luca di Montezemolo reportedly left the Bahrain circuit early on Sunday night after saying Ferrari's performance was "very painful."
While Mercedes raced into the distance, claiming a second successive 1-2 result, Ferrari were unable to even join the podium.
Outpaced by Force India, Williams and Red Bull, Fernando Alonso and Kimi Raikkonen eventually finished ninth and tenth respectively.
However, Ferrari President di Montezemolo was not on hand to witness the double points-finish having already left the circuit.
"I don't like seeing Ferrari in this condition," F1 journalist James Allen reports di Montezemolo as having said to the Italian media.
"The engine people at the factory need to work to make a big leap forward in quality.
"I didn't expect much from this race, but I did expect a bit more than this.
"To see a Ferrari this slow on the straights is very painful."