Sir Alex Ferguson's side failed to win any silverware for the first time since 2005 after being pipped to the Premier League title by Manchester City on a dramatic final day.
Anderson admits not winning anything was not good enough but expects this summer's new signings will help rectify that.
"We have to do better. Manchester United has to win every trophy and we're disappointed if we don't," he told the club's official website. "There's always pressure to do well when you play for this club.
"Last season we lost the league on goal difference and everybody was sad but we have to forget that and concentrate on this season. At the beginning of the season it's always difficult but we've got a couple of wins and now we want more.
"Shinji Kagawa and Robin van Persie have a lot of quality and they make it easier for the rest of the team when they have so much talent. It also means everybody works harder to try and keep their own place."