The midfielder is used to winning Premier League titles at Old Trafford, having won five times under the reign of Sir Alex Ferguson so ending up out of the top three felt slightly foreign to the 33-year old.
Carrick said: "Fourth place is an achievement but it's not that great. Finishing seventh was a real blip and it was a one-off.
"This club belongs in the Champions League and we can't get too carried away with making it because we should be there anyway.
"We're certainly satisfied in some ways because of last season, but next season we want to look up and not be settling for fourth.
"We had mixed results at the start, picked up for a while, dipped a bit, picked up again and then had another dip. But there are certainly signs of moving in the right direction and signs of big improvement.
"All in all, we can be satisfied with getting in the top four, but it's not worth celebrating. Hopefully we can do a bit of celebrating next season."