Vasquez's header three minutes from time settled a tight tie at the Ferraris, sending Genoa through to face holders Inter in the next round. Speaking to Mediaset, De Rossi said he had seen what he needed from a much-changed line-up that included several fringe players.
"Yes, everyone put in their performance and the attitude was right," De Rossi said. "Some of the lads' condition was shaky, that's why I played them. Winning was important, we don't want to snub the Coppa Italia, and playing against Inter is a nice thing."
Asked about a banner from Genoa's ultras reading "everyone to Parma," a reference to an upcoming away trip, De Rossi praised the connection with the club's most vocal supporters.
"They're described as the most fiery section of the fanbase, but really they're the ones who understand us best," he said. "It's nice to feel them close ahead of Parma."
On the character of his squad following a summer of turnover, De Rossi struck a measured tone.
"It's a squad of serious lads, who care a great deal and go for it. We've lost some important characters and we need to build their physicality, their tactical side, but also new leaders to get the points we need," he said. "We already have them - Baldanzi is taking on more responsibility than last year. We need to do more and not wait until we're in trouble. That's on me to work on, but they really are exceptional."
De Rossi also highlighted a string of fringe players given minutes, including Traore's introduction and El Shaarawy's appearance from the bench.
"I also want to mention other players who played their first matches, like Puczka, Amorim and Wiafe. Drameh arrived on August 31, Mitaj has done very well," he said. "Traore is a different type of player - he needs a bit more to play a full match, but he can change our season alongside Stephan. He's a bit further ahead and could be ready before Ahmed."
Asked whether he expected to find Cristian Chivu doing so well as a coach, De Rossi admitted he wasn't entirely surprised, recalling that Chivu had played against his father at Primavera level.
"We're always in touch, I knew he had this passion, and he'd played against my father in the Primavera," De Rossi said. "He did well at Parma, but going from doing well to winning the title and the Coppa Italia in your first year is something that will happen rarely, I think."