United missed out on a 20th league title in the dying seconds of the season as Sergio Aguero fired rivals Manchester City to their first championship since 1968, while a disappointing European campaign saw them exit the Champions League in the group stages.
However, Vidic believes that United will be stronger for those experiences, having learned some valuable lessons.
"We had some young players play a lot of games last season and they'll have learned a lot. We all learned," said Vidic.
"In Europe we've had so much success in recent years - we've had three finals, a semi-final - and maybe we relaxed a bit last season. We were punished and we can't allow that to happen again. We had a few injuries last season too. I hope everyone can stay fit this season.
"The young players can learn from last year, so I'm confident we'll be better this year."
Vidic spent much of last season on the sidelines through injury, but recently made his return to the first team in a pre-season friendly.