The Nerazzurri veteran celebrated his comeback from a six-month absence on Saturday and hopes to have achieved something "important" in the near future.
The Argentine dynamo came on as a substitute for the first time since rupturing his Achilles tendon in a loss to Palermo in April, sparking the move that led to Yuto Nagatomo's strike.
And Zanetti is hopeful his presence will spur the Nerazzurri on to achieving something for the fans, after their support proved crucial to making it back at 40 years old.
"We want to be challenging for something important. I don't know what exactly but I know we can go a long way," he told reporters after the match. "It wasn't easy coming back at the age of 40 after six months out. But immediately after my injury I said I wanted to come back and play in front of my fans again.
"I want to thank the fans for all the love they've shown me, as well as the president and coaching staff who have given me so much support. I'm pleased to be back and that it coincided with an important win. It was a great feeling."
Zanetti is Inter's record Serie A appearance holder after playing in over 600 games for the San Siro giant and was part of the 2010 side that secured an unprecedented treble.
Despite not playing in Europe this season, Walter Mazzarri's men currently lie fourth in Serie A, six points behind leaders Roma who play on Sunday.