Quique Setien’s side were beaten by a very late goal from Inaki Williams after an intense 90 minutes at San Mames that saw the visitors spurn some good chances to score.
Frenkie de Jong will also feel he should have been awarded a penalty in the second half, and Busquets felt his team deserved to progress.
“It’s a sad day for everyone. We didn’t want to go out. We have two competitions left, we have to keep on fighting. We have to continue. Everyone’s angry. We did things well,” he said..
“We deserved to go through, but this is the new Copa. In one isolated moment, it can slip away from you.
”A fateful ending after all that happened. That’s football. One cross has ended up in the back of the net. We’d managed the game well, we knew how to suffer but one detail and you’re gone.”