The Argentine skipper was quite pleased with his side's win, while Esteban Cambiasso was equally happy with the Nerazzurri's performance
The Nerazzurri have climbed to third spot in the Serie A table following this weekend's results, and Zanetti has made it clear that they're ready to battle for the top spots.
"The league table is starting to look the way it should now and we'll push on. Milan are next up [in Serie A] and they'll be faced by an Inter side that will be really up for it," Zanetti was quoted as saying on the official Inter website.
"It was all about getting the win [against Fiorentina] and I think we were particularly good in the first period. We could have gone in with our noses further in front.
"We're in the mix now though, we're aware of our strengths and ready to keep battling."
Midfielder Esteban Cambiasso was equally pleased with his side's performance, and stressed that Inter are still a work in progress.
"The first half was really good and I don't think anyone would have been surprised if the game had finished 4-1. Regardless of how well we did tonight though, we've never lacked the desire or the right approach.
"You just get days when you play better and others when you can't quite manage it. We're a developing team: [Andrea] Stramaccioni has very clear ideas of what he wants and we're following him."
Inter resume match action on Thursday when they take on Neftchi Baku, before locking horns with arch-rivals AC Milan on Sunday.