The Viola trailed 2-0 after 65 minutes before a hat-trick from Giuseppe Rossi inspired Fiorentina to a long-overdue win against Juventus at the Artemio Franchi stadium.
"Florence awaited this win for 15 years," Della Valle said to www.acffiorentina.it.
"We dedicate this victory to the city and to the fans, who deserve all this joy.
"It has been a great win against one of the strongest Juve sides I have ever seen.
"Now we must maintain the same spirit that allowed us to come back against Juventus."
Della Valle hailed Serie A's leading scorer Rossi, who has been crucial in Fiorentina's fine start to the campaign - the Viola have won four and lost just one of their opening eight league games.
Rossi joined the Florence outfit this summer from Spanish side Villarreal having recovered from serious knee injuries that had ruled him out of action for almost two years.
The Italy international has scored eight goals to help the Viola climb to sixth place.
"We have a lot of belief in Rossi and for us, he has always been a certainty," Della Valle said.
"Perhaps others saw his signing as a risk."
Fiorentina host Pandurii in the Europa League on Thursday before travelling to Verona to face Chievo three days later.
The Viola, coached by Vincenzo Montella, will be hoping to recover veteran midfielder Massimo Ambrosini, who sustained a muscular injury on Sunday.