The Red Devils secure qualification for next year's Champions League with their 3-2 win over Liverpool earlier this month, but Carrick - United's interim head coach - has denied suggestions that his side now have nothing to play for.
Asked whether complacency was a factor in United's lacklustre draw with Sunderland over the weekend, Carrick replied: "I honestly get offended by that, when people are accusing you of that.
"The way the players have prepared for the game and the way they left the changing room, we faced a tough game. It's fine. If we weren't in a good head space and motivated, I think we lose the game today."
Carrick opted to give credit to Sunderland for United's underwhelming performance.
The former England international - who is in contention to become United's full-time coach, following the departure of Ruben Amorim in January - said: "Sunderland played really well at certain points of the game and made us work for it.
"I think the fact of our pride in ourselves and each other, the responsibility playing for this great club, to be part of it, certainly motivation and focus is not a reason why we we're going to be brilliant or maybe have a performance where it becomes a little bit more challenging. Whether that's today or the next two games, that won't be the case whether it's affected it."
Casemiro missed the Sunderland game with a minor injury. But with the Brazilian set to leave the club this summer, Carrick admits that they need to strengthen in the midfield area.
He said: "It's not just totally on one game or two games, I think we're always assessing the direction of the player we need to go.
"It's not judged on that but in time, you get a clear picture of what it looks like, some positives and some negatives, what we need to improve on.
"Certainly, today or next week or the week after, that's not a total decisive factor over making decisions, it needs a lot more foundations and foundations than that to make decisions over one or two games."