Alberto Gilardino's goal in the second half proved to be the difference between the two teams at the San Siro.
"We needed a convincing performance from everyone," Zanetti told Inter's official website. "We all must try and give more.
"Bologna were better than us in the first half, we attacked more after the break and showed greater fight, but then they scored. It's a tough time, you lose a bit of belief when things aren't going well.
"We now need this to end as soon as possible because it can't continue: we need to rediscover our confidence. We're working on it but it's not easy."
Inter are currently fifth in the Serie A table with 47 points from 28 matches.