Responding to praise that was heaped on the Spanish driver last week by Mercedes chairman Dieter Zetsche, Alonso said: "it's sometimes strange to see good comments and compliments from people from outside, and the opposite from people who are supposed to be close to you."
Alonso had a strained relationship with Ferrari last year, and Di Montezemolo does not need any more controversy as his team struggles to keep up with runaway leader Mercedes.
"Fernando is the best driver in the world, who always gives 200 per cent. He knows how much I count on him, even away from the race track, in terms of his contribution and the impetus he gives to the team," Di Montezemolo said in a statement Thursday. "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."
Zetsche had told Spanish media: "Alonso is probably the best driver on the Formula One grid. Fernando has always proven it — and in uncompetitive cars."
Relations between Alonso and Ferrari have sometimes been strained. Alonso was given a public rebuke from Di Montezemolo for comments he made after the Hungarian Grand Prix last July.
The day after that race, where he finished fifth, the Spaniard was asked what he would like as a 32nd birthday present and responded with an acerbic "somebody else's car."
Rather than keep it as an internal affair, Di Montezemolo stated he had "tweaked the ear" of Alonso.
Alonso has not won a race since last year's Spanish GP — a barren run of 19 races — and he has finished on the podium once so far this season, at last month's China GP. He is third overall, 51 points behind Mercedes driver Lewis Hamilton.
"The truth is that he and Kimi, another incredible driver, need a competitive Ferrari and giving them that is our sole objective," Di Montezemolo said. "We are working very hard."