Only Wayne Rooney's late consolation prevented United suffering the worst two-legged European defeat in Ferguson's entire time as manager.
The Red Devils won just three of their 10 games in UEFA competition and suffered a hat-trick of losses for the first time since 2004.
It represents a startling fall from grace for a team that had reached three of the last four Champions League finals and Ferguson admitted he has some work to do to find out where it all went wrong.
"Trying to analyse this season against others is a bit difficult," he said. "There is a route in terms of some of the goals we have lost in these tournaments. They have been pretty poor.
"It has been a disappointing year."
However, having assumed the Premier League leadership last weekend and knowing they will open the gap on nearest challengers Manchester City to four points if they win at Wolves on Sunday, Ferguson realises this is no time to get too downhearted.
"Feeling sorry for myself is not an issue for me," he said. "There is a disappointment but analysing the performances is more important and we have an important game on Sunday."
Ferguson confirmed his decision to replace Rio Ferdinand, Michael Carrick and Ryan Giggs in the second half was purely to keep them fresh for the trip to Molineux.
The Scot had long since abandoned any hope of reaching the quarter-finals as, trailing 3-2 from the first leg, United fell further behind thanks to Fernando Llorente's excellent volley before Oscar de Marcos doubled their lead in the second half.
Rooney's 27th goal of the season 10 minutes from time came far too late to have any effect on the overall outcome.
"I don't think we can complain at the result," Ferguson said. "In the second half in particular, Bilbao were the better team.
"Their first goal was a bad one for us to lose. You can't believe an English team would lose a goal like that to a long ball. Ours was too late to do anything about it."
Ferguson praised Athletic Bilbao for their performances over the two games and admitted he hoped they now went on to win the competition.
"Athletic could do very well," he said. "What we have seen, tonight [Thursday] and last Thursday, is a team whose workrate is higher than anyone I have seen in Europe.
"That takes you a long way but it is not just about their workrate. They have some fantastic qualities also.
"I would like to wish them well. I hope they do win it because it is a testament to the hard work they all put in, from their coach right through.
"They have created a cause. Such energy and determination to win football matches is an incredible thing to see. They deserve to win it."
Athletic coach Marcelo Bielsa said he was delighted with the victory but as English teams suffered more trauma in Europe, with only Chelsea's amazing victory over Napoli providing some respite, the South American refused to enter a debate about whether the British game is too insular.
"Victory against a team like Manchester United cannot be ignored," he said. "But I don't have any reason to think it has happened because English football is too insular."