After three rounds, Hayden and Rossi are eighth and ninth in the championship standings, with 23 and 22 points respectively.
At the same stage last season, the pair were fourth and fifth, with 31 (Rossi) and 30 (Hayden) points.
Preziosi insisted Ducati remains determined to create a motorcycle that suits seven time MotoGP champion Rossi.
“We believe that a bike Valentino likes, is a good bike for all riders,” he said. “We are following the direction he suggests at the best of our capability, which is not enough right now to be faster than Honda. But for sure we will try in the direction that Valentino shows us.”
In terms of machine set-up, Preziosi said that Rossi and crew chief Jerry Burgess always have the final say.
“We give Jeremy 100% freedom to define with Valentino what the best set-up is. As Ducati, our duty is just to supply material.
“We can suggest what our ideas are, but the final decision, day by day, practice by practice, is made by Jeremy speaking with Valentino."
Round four of the MotoGP World Championship, the French Grand Prix, takes place on May 18-20.
Le Mans was the scene of Rossi's only Ducati podium to date.