Last season's Champions League finalists dropped into Europe's second-tier competition after failing to navigate their way through the Champions League group stages.
After successful progression past Ajax in the previous round, United met their match against Athletic Bilbao in the last-16, and after being condemned to a 3-2 defeat at Old Trafford in the first leg, the Premier League side travelled to Spain needing a 2-0 victory in San Mames to make it through to the quarter-final stage.
Those plans were shattered when Fernando Llorente volleyed home for Bilbao after only 23 minutes, helping the Basque side on their way to a 2-1 win, taking them through 5-3 on aggregate, and leaving Ferguson bitterly disappointed.
"There are always lessons to learn from every football match, whether you win or lose," he told Channel 5 in his post-match interview. "It's disappointing more than anything.
"We haven't progressed in the Champions League and now we're out of the Europa League. I think the best team went through. I don't think we can complain.
"They got a really soft goal to put them ahead and that's the last thing we wanted. I can't believe we lost a goal like that. It was a really poor one.
"Otherwise, I thought it was quite even in the first half. I thought we did quite well. But at the start of the second half Bilbao did very well. They could have scored two or three goals.
"Towards the end we had a bit of impetus - we scored a goal but we didn't get anywhere near to winning it."
Their surprise exit means that Manchester United can now concentrate fully on the task of retaining their Premier League title, with a direct head-to-head battle with local rivals Manchester City.
However, Ferguson warned that the club's domestic challenge will not be any easier after their European omission, and has called for his players to stick together and bounce back at the weekend.
"It's not a sense of relief [going out of Europe] because we still have 10 games to play [in the league] and that's a long way to go until you can win a title," he added.
"Obviously we now have to make sure we win on Sunday against Wolverhampton Wanderers. We decided to take off Rio Ferdinand, Michael Carrick and, eventually, Ryan Giggs because we have to think about Sunday."