United dropped into Europe's second-tier competition after falling at the first hurdle in the Champions League, but Carrick has reassured fans that the Red Devils will do all they can to lift the trophy.
"It is still a European competition,” he told the club’s official website.
“It is one we are desperate to win. We have never really been part of it. Who knows when the chance to win it will come round again?
"We want to grasp it. As players and, as a club, we are determined to go far.
"It doesn't take much motivation from the players' point of view. 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."
Sir Alex Ferguson's men have been pitted against Spanish outfit Athletic Bilbao in the last 16 and the 30-year-old midfielder believes Marcelo Bielsa's side are more than capable of causing problems.
"Bilbao is a tough place to go, we need to perform well at home to give us a chance in the away leg,” he explained.
“Most of the time in recent years we've tended to play the away leg first. That will be something different for us. It won't change our approach hugely but we know how tough it will be over there.
“It is renowned to be a very hostile environment. They have fanatical fans but it's something we're looking forward to.”
The former Tottenham man also spoke of his side's uncharacteristically bad home form in Europe this season, which most recently saw them lose 2-1 to Ajax at Old Trafford.
"I'm not sure why our home form in Europe has not been so good," he added.
“It's a tough one. We haven't quite performed on the night for whatever reason.
“Compared to recent years, when our home form has been formidable, it hasn't quite happened for us this year. That's the reason why we're talking about the Europa League.
“The Ajax game was a bit of a disappointment but we got through. We can put that behind us and look forward."