Goals from Nicolas Raimondo, either side of a Riccardo Bracaglia strike, sealed a result far more emphatic than the balance of play suggested, according to Alvini himself.
"On such a beautiful and important evening, I want to send a message to the community of Fucecchio, who yesterday lost a well-known local figure - Gianluca was a great person and I dedicate this win to him," the Frosinone coach said.
"As for the match, I'm happy because it wasn't easy, and the result was wider than what we deserved - Fiorentina made it a tough game."
Alvini insisted his side's approach would not change against bigger opposition.
"We try to always play like this, even against Juventus. We have our own identity - then it depends on the match, you can win or not, but there's always the desire to do well," he said, rejecting the idea there was any secret behind the result.
"There's no secret. What counts is the daily work and the availability the players give you. The transfer market drains energy, and I have to compliment the players."
Asked whether winger Fares Ghedjemis had now definitively made the position his own, Alvini pointed to a broader philosophy: "I don't think taking Fiorentina back into their own penalty area gets you the result, so it's good to try to play. It's important to have clear ideas and communicate them. I don't decide on the transfer market - I decide on the pitch, in the daily work."
Fiorentina boss Fabio Grosso struck a far more downbeat tone.
"On a day like this we wanted to do something different. We showed too much carelessness and fragility, both in character and structurally - the base on which quality has to rest, and we were also able to show that quality. We're disappointed, there's still a lot of work to do and we have to raise our level, because Serie A doesn't wait for you," he said.
Asked where the blame lay between the transfer market and his own team's performance, Grosso pointed to detail rather than excuses.
"Some things came through for me today and we have to be good at building on them. The numbers say it was a different game to how it finished. We lacked the right energy to stop our opponents hurting us."
Pressed on his line about having "pictures with no walls to hang them on," he explained: "We showed quality but not the solidity for that quality to rest on. We weren't sharp enough to finish with the right ferocity, and Frosinone were better than us at doing that. We need to raise our appetite to stay in the game, to resist the opposition."
On the decision to leave Moise Kean out of the squad entirely, Grosso added: "I'd have liked to have had him, even for a spell, because his energy would have been useful. In a few days the noise will settle and we'll understand who we are, and get to work hard."