"You work to win. This job would be the best in the world without matches," Gattuso told the club's official channels after the victory, Lazio's final test before their Coppa Italia opener.
"We're happy, there's room to improve, but Frosinone go very well and we did well to keep pace with them. We could have done better in the final 25 metres.
"I'm very satisfied with what this team does in training. I'll keep the good things to work on what to do - we need to be cleaner."
Asked about the team's reaction after conceding an early goal to Salvatore Calo before fighting back through a Mattia Zaccagni brace, Gattuso pointed to a shift in mentality from a year ago.
"It's not by chance. Zaccagni last year would have let himself get carried away today - I want that to be the attitude of this team. We have to be good. The team is moving well, we have legs. We still need to shake off some of the physical load, but if we want to play this way we have to go for it, if we sit back they'll make us dance the rumba.
"This is the path, we can't go slowly. Playing with a back three? We can do anything, it depends on the opponent. We have to try everything, we'll use that system too."
Gattuso also addressed Lazio's pursuit of AC Milan forward Santiago Gimenez, making clear the club's approach to transfer targets.
"The most important thing is that the people who come here want to come. I'm not used to convincing players, in football you can't promise anything, the pitch does the talking. If someone wants it, they have to come and put the helmet on, that's what we need this year. If those conditions aren't there, it's pointless."
The head coach was more direct on why a deal for Ivanovic, the Croatia international striker Lazio had been chasing, fell through in favour of a move to Lens.
"Let's not beat around the bush. You know how it went with the striker, the club did everything to get him and I spoke with the player. Benfica had given the green light, he decided to go to Lens to play in the Champions League. What can we do? Nothing. Maybe we got it wrong, we should have spoken to the player first."
Gattuso offered a similar explanation for the failed move for 19-year-old FC Nordsjælland defender Noah Markmann, who turned down the club.
"The same goes for Markmann - a 19-year-old asked me to play as a starter, football is changing. We can't just sign players for the sake of it, we need players who are functional to how we want to play. I've taken the blame, that's a fact. I want functional players. When these things happen there's a lot of regret, but now we're getting back in motion and we'll find those two profiles. When the striker arrives, we'll see."