The Red Devils were eliminated from the Champions League earlier in the season for only the third time in 17 years by Switzerland’s FC Basel, meaning they were forced to experience Europa League football for the first time.
Sir Alex Ferguson’s men face Spanish side Athletic Bilbao in the last 16 after defeating Ajax in the previous round, and Carrick believes they can win the competition despite facing a battle with rivals Manchester City to retain the Premier League title.
"It doesn't take much motivation from the players' point of view,” he said on the club's official website. “It's a competition we want to win, I want to win it.
“I've never played in this competition. We are still desperate to go as far as we would do in the Champions League."
Despite being installed among the favourites for the competition, the 30-year-old believes that their Spanish opponents must be treated with respect.
“Bilbao is a tough place to go," he added. "We need to perform well at home to give us a chance in the away leg.
“It is renowned to be a very hostile environment. They have fanatical fans but it's something we're looking forward to.”
By Matt Maltby
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