Ivo Pulga and his assistant manager Diego Lopez have defied expectations in guiding the Isolani to four straight wins since replacing Massimo Ficcadenti in October.
The Sardinians last won four on the spin in the 2009-10 season, but a run of five consecutive wins has eluded the club since their promotion to the top flight in 2004.
Fiorentina are in buoyant mood too, having moved into fifth place courtesy of a first away win of the season at Genoa on Thursday.
Astori told the Corriere dello Sport: "We have to enjoy the moment but not let it go to our heads.
"Our two bosses, Pulga and Lopez, are doing extraordinary work.
"The former spends a lot of time talking to the players and the latter gives us a lot of advice on defending.
"Most of all, they have brought back confidence and enthusiasm when we had all lost our conviction.
"We are playing well and the results prove that, we are all behind this project.
"It will be important not to take anything for granted, though, or it will all come tumbling down."
Cagliari, who saw off the threat of Siena in midweek, are without suspended pair Daniele Conti and Radja Nainggolan.
Manuel Pasqual's classy lob proved enough for Vincenzo Montella's Viola to climb into the European places, and midfielder David Pizarro is already excited about a potential return to continental competition.
The Chilean told the Corriere dello Sport: "We struggled against a tough team, Vincenzo asked us to get an away win and we did it, so we're more than happy.
"We are doing some great work, it's difficult to keep up but we're trying our hardest.
"The objective? I miss playing in Europe so I hope we can bring it to Florence."
Concern surrounds Montenegrin striker Stevan Jovetic, who has now gone three games without notching, but Pasqual's strike from left-back proves Fiorentina can produce goals from unexpected sources.