Inter finished ninth last term, their worst league position since 1994, and two poor seasons in a row will not be accepted by the club's supporters.
New manager Walter Mazzarri has arrived from Napoli, as have a host of new young players.
"We must start challenging again," Zanetti said.
"We have to bounce back this season and to do that we need a strong group of players.
"He (Mazzarri) is an expert coach with clear ideas. To be a great team you need a charismatic tactician and Mazzarri is that.
"We've also got more experienced heads and youngsters we have high hopes for – it's the right mix to help us come back stronger than before.
"We're here to help the younger players because they represent our future – that's why we're placing our faith in them."
"I don't know when I'll be able to make my comeback, but I'm working hard to make it happen," he said.
"At the end of the season I'll decide whether to hang up my boots or whether I have enough left in me to carry on.
"When I do stop playing I hope to be as useful to Inter off the pitch as I've tried to be on it."
