Barcelona lost their La Liga and Champions League crowns to Real Madrid and Chelsea respectively last term.
The Catalan club triumphed in the Copa del Rey, but their 3-0 win over Athletic Bilbao in the final was Pep Guardiola's last match in charge and he was replaced by assistant Vilanova.
While midfielder Iniesta is champing at the bit for more silverware, he thinks it will come only when the players pull in the right direction.
"The manager has changed, but the main responsibility still lies with the players. It's our responsibility to give everything to keep this working," the 28-year-old told the club's official website.
"The key to everything has been finding the right balance and we have all gone in the same direction, not just the players but everybody around us.
"Although we've been together for a few years, his (Vilanova) responsibility isn't the same any more.
"At this club we always demand the very best possible, this year the same as any other. The important thing is for the team to be as hungry as ever."
Barcelona will get their season under way with the first leg of the Supercup against fierce rivals Real in two weeks.
"We treat them as very important, although they won't decide the season. But whoever wins will gain more confidence," said Iniesta, who helped Spain defend their European Championship crown in Poland and Ukraine this summer.
Barcelona have been boosted by David Villa's return from a broken leg that ruled him out of action for eight months.
Iniesta has welcomed his comeback and hopes it is only a matter of time before the striker returns to form.
"He looks great to me considering he's been injured for so long," Iniesta added.
"It's lovely to see him training because he's such a fundamental player and we hope it won't be long before he's back doing what he does best - score goals."