After nine matches of the campaign, Valencia sit fourth in La Liga, just two points off leaders Barcelona.
"The fans always show a special affection towards us. I haven't always had the happiest of times here but they always stuck with me," Piatti told reporters.
"It's evident that when the fans are with us, it makes things easier for the team on the pitch."
Valencia recorded a 3-1 win over Elche at the weekend.