United endured a dismal 2013/14 campaign, finishing in seventh place in the Premier League and failing to land any major trophies.
The club is about to start a new era under Louis van Gaal and have recruited England full-back Luke Shaw and Athletic Bilbao's Ander Herrera over the past week.
Carrick was frustrated with United's inconsistent form, costing them Champions League football, but still believes his team-mates can compete with the top sides in England.
"Yes, it's not a nice feeling when things don't go right," the midfielder told Sky Sports News. "You give your best as everyone did, sometimes it just doesn't go for us and that was the case over too long a time really.
"You have dips and you expect to get over them quick - and at times we showed that we were going to get over them - and then just as results and performances were changing we took a step back again. That was very frustrating.
"Looking back it was a disappointing campaign, but we’ve got to learn from it. Never stop learning and take what we can.
"We've still certainly got enough quality in the squad anyway, regardless of who is coming in this summer, to be up there challenging again."
Van Gaal is likely to make more changes as he attempts to transform United into genuine title contenders.
And Carrick, a long-serving player, will maintain the same desire to impress during pre-season.
"I'm not going into this season any different to how I have any other," he said.
"Whether you win or lose, I’ve said it before when we’ve won things, the next season you've got to start again, doing it all over again.
"Last season counts for nothing, for everyone. We go into this fresh and really positive and looking forward to a successful campaign."