The Argentine veteran commented on the Nerazzurri's important 1-0 win in Serie A, and has set his sights on a positive start to the new year
The veteran defender featured in the match, which was decided by a goal from Japanese left-back Yuto Nagatomo in the 67th minute.
"[It was] an important test at a difficult ground," said Zanetti, according to Inter's official website. "We needed a win like this. We risked almost nothing and we were also dangerous many times.
"The important thing was having seen a very solid Inter that knew how to play their game."
The win over Genoa at the Stadio Luigi Ferraris moves the Nerazzurri up to seventh place, with the former European champions now sitting 10 points behind league leaders Juventus.
"Are we now more relaxed when looking at the table? We're following our own path and not looking at the standings," said the Argentine.
"There are still two games left before the break. Let's see where we are at Christmas and when we resume we'll see about continuing this streak of victories."
Inter's next league fixture will be away to 18th placed Cesena on December 18.