Sannino's men followed their 1-1 draw against Napoli with Wednesday's 1-0 triumph at Chievo to reach the last four of the Coppa Italia for the first time in the club's history.
Siena will meet Napoli in the two-legged semi-final.
In the meantime, the Bianconeri will have the added motivation of knowing that a win on Sunday could see them go level on 22 points with Fiorentina.
Siena lie 17th, four points clear of the drop zone.
"I complimented my players because they did a great job in Verona," Sannino said. "We showed great determination to win away from home and without our fans.
"We did our duty which was to progress to the next round without conceding a goal.
"We are trying to improve on the road.
"But now we have to think about the match at Fiorentina, which will be another test for my players.
"We have to continue on this path without getting too carried away by our results of late."
Sannino has reason to be wary for his side have not won on the road in Serie A this season.
Siena will be bolstered by the return of defender Luca Rossettini and midfielder Alessandro Gazzi from suspension.
Fiorentina, meanwhile, will be looking to inflict Siena's fifth straight defeat on the road.
The Viola bolstered their attacking line with the arrival of Amauri from Juventus this week.
The 31-year-old striker is expected to make his debut at the Stadio Artemio Franchi this weekend.
"I am delighted to be here and looking forward to play," Amauri said.
The Viola need all the help they can get up front as they have failed to find the back of the net in their last two league games.
Delio Rossi's side have won just one of their last six league games and last weekend's goalless draw at Cagliari left them in 13th place.
The hosts will be without suspended midfielder Gianni Munari.