Alonso responded by saying it is "curious" that rivals heap praise on him, while only "opposite" feedback comes from those in his inner circle.
It was interpreted as a clear sign that Alonso's patience may finally be up with the Maranello team, five years after Ferrari promised him a title-winning car.
But Ferrari president Montezemolo reacted swiftly, with his comments made at Maranello promptly emailed to journalists and posted on the team's official website.
"Fernando is the best driver in the world, who always gives 200 per cent in the races," he said.
Montezemolo said Alonso "knows" how highly he rates him.
"I think it's incredible that there are still some so-called experts who don't understand that and are always looking for a polemical situation that simply doesn't exist," he added.
The apparently increasingly-frustrated Alonso had also said in Monaco that he had noticed no recent improvements despite the arrival of new boss Marco Mattiacci.
Montezemolo, however, said Mattiacci will in fact "instigate many changes at a technical and organisational level".
"That's what I want, as do our drivers and our fans, while all the rest is just idle chat," he concluded.