The Reds will finish this season in seventh spot and, despite the disappointments of slipping down the table and out of the Champions League, Carrick is setting his sights much higher than fourth position next time around.
He said: "There is no way we are settling for top four. That is not something we do here.
"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."
As for looking ahead to next season and a new manager, he went on: "It is easy to say there will be wholesale changes because obviously we haven't had a good season.
"But if you look within the squad, there are some good players here. There probably needs to be some changes in some way because that is natural with the situation we are in at the moment but you can't change too much because it is hard."