A pair of late goals gave the Spanish side a 3-2 second leg win at Pittodrie and a 5-2 aggregate success, but the Scottish team gave a fine account of themselves.
Having fallen behind to an early Xabi Prieto goal, the Dons took the lead through Peter Pawlett and Mark Reynolds, but Prieto levelled with a late penalty and Markel Bergara then won it with an injury-time header.
And McInnes says Aberdeen now need to make sure they are back in Europe next season.
"What it's done is whet the appetite to play more European football in the future,” he said.
"To do that we need to have a good campaign again, and that's exactly what we intend to do this year.
"When we went 2-1 up, I think people were starting to think 'here we go', for the first time in the tie, but it was too frantic for my liking.
"We played the last 20 minutes like you might play the last two or three normally.
"We made a couple of substitutions we wouldn't ordinarily make in order to try and get the next goal, but they're a good side and I expect them to do well, so there's no shame in losing to them, and only pride in what we've achieved.
"I'm immensely proud of the players' efforts.
"It was a real tough draw for us, but the fact we're disappointed is recognition of what a magnificent effort it was from the players."