Luca di Montezemolo pointed his finger at Pirelli on Saturday as he slammed an "odd" qualifying session at Valencia.
A surprise and rare visitor in the Ferrari garage, team president Montezemolo was bitterly disappointed after neither F2012 made the Q3 cut.
"We were fastest and then everything changed when we put on the soft tyres," he told Italian broadcaster Rai.
"We need to take care that this does not become a tire manufacturing championship," Montezemolo warned.
Fernando Alonso, however, insisted that the main problem in his native Spain was that the red car was simply "not fast enough".
But there were others casting a wary glance in Pirelli's direction, including Jenson Button, who qualified just ninth despite earlier looking to have emerged from his performance slump.
"All the way through the pace was very good, and then we put on a new set at the end, came out of the pits and turned into turn one and I had no front grip," said the McLaren driver.
"I don't know why that is, but it's something I've definitely got to find out about because I don't think the circuit changed that much between runs."
Former grand prix driver Taki Inoue sounded positively unimpressed.
"Another different lottery winner can be expected at Valencia. 2012 seems to be Pirelli gambling. This is not F1 any more. Boring!" the Japanese wrote on Twitter.
Force India boss Vijay Mallya disagrees completely.
"Formula one has become so very competitive, exciting and unpredictable," the Indian billionaire said after qualifying. "Not because of the genius engineers in teams but the Pirelli tyres!"