Tommaso Rocchi's second-half goal proved enough for the Nerazzurri to pick up maximum points at the San Siro.
"We got back to winning at home again," Zanetti told Inter Channel. "These are three important points after a run of poor results.
"Considering the period we've been in we truly deserved this win. It was a hard-fought game. They had a few chances but we gave little away.
"We had to take advantage of every bit of space because they close down and hit you on the break. It was difficult but we did a good job finding the right spots."
Inter are now fifth in Serie A with 53 points from 33 matches.