The reverse - Samp's second defeat of the campaign - left the Blucerchiati in 17th place, with just one point after three games.
Rossi was fuming with his side's 3-0 loss and is looking for an immediate reaction.
"I cannot believe how bad we were, it was unacceptable," Rossi said. "In the game that matters most to our club and to our fans, we let them down.
"Genoa deserved the win. We must react immediately.
"We have a lot of work to do and we now need to get our hands dirty in order to find the fighting spirit that we lacked against Genoa."
Lack of goalscoring has been Samp's main problem so far with Rossi's men having found the net just twice in three games.
To complicate matters for Samp, Rossi is without striker Eder, who will be out of action for two weeks having sustained a knee injury against Genoa.
Cagliari go into Saturday's encounter at the Nereo Rocco stadium inspired by Mauricio Pinilla's stoppage-time goal which gave the islanders a deserved share of the points at Fiorentina in the last round.
The Sardinian outfit will now be hoping to build on that result and claim their second win of the campaign against Samp.
"We have to continue to work hard and make the most of our chances," Cagliari coach Ivo Pulga said.
Cagliari are still playing their home games in Trieste until they return to the Sant' Elia stadium that is undergoing restructuring.