United were bundled out of the Champions League by Bayern Munich last night.
Carrick lamented: "It was always going to be tough tonight, but the reason we may not be in the Champions League next season is not so much because of tonight or last week - it's down to our league form through the season. We take responsibility for that.
"It's been over a long period of time that we've had too many bad results and no Champions League football is the price we pay for that. This is where we want to be - this is where we've been for a long time - and I'm sure we'll be back here in the not-too-distant future."
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