Ferguson said: "It's not a sense of relief [to go out] because there are still 10 games to play in the league.
"It's disappointing that we haven't progressed in the Champions League and we are out of Europa League now."
Last season's Champions League finalists slumped to a 2-1 defeat thanks to goals from Fernando Llorente and Oscar de Marcos, to follow up a 3-2 loss at Old Trafford last week.
And they were once again taken apart by Marcelo Bielsa's team in a superb display that left the Stadio San Mames rocking.
Ferguson conceded that his team were second best in the Europa League clash.
"At the start of the second half they did really well and could have scored two or three more goals.
"We did better later on but nowhere near enough to win."