The reigning Premier League champions have fallen from grace in 2013/14 by dropping to seventh place on the table in what has been an extremely disappointing campaign.
The Red Devils will be out of the Champions League next term but midfielder Carrick feels the goal of only returning to Europe's premier club competition is not high enough for such a proud club.
"There is no way we are settling for top four. That is not something we do here," said a defiant Carrick.
"We can't celebrate getting into the top four, that's not worth celebrating. We want to be challenging right at the top.
"I am not saying we are going to win the league next season but that is what our goal is and anything less is not worth thinking about."
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