The Brazilian underlined the high expectations at Old Trafford and maintained that the club should challenge for every trophy, insisting he welcomed competition from new signings
Manchester City won the title on the last day of the season, finishing above United on goal difference, while the Red Devils failed to qualify from their group in the Champions League and left the FA Cup at the fourth round following a defeat away to Liverpool.
"We have to do better," Anderson told the club's official website. "Manchester United have to win every trophy and we're disappointed if we don't.
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After losing their first match of the season to Everton, the Red Devils have won each of their last two league matches at home against Fulham and then away at Southampton, with new-boy Robin van Persie scoring four goals in the two games, and Anderson says the new arrivals are great players.
He added: "I think the team looks good. 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. 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."
Anderson has struggled for game time at Old Trafford, having encountered several injuries since his arrival from Porto in 2007, but started their last match against Southampton.