Osasuna won 3-2, with Aimar Oroz and Ante Budimir (2) hitting the goals for the visitors. Nico Williams and Oscar de Marcos struck for Athletic.
Afterwards, Moreno said: "I had no doubt that we were going to stand up to the challenge. A big opponent. A big stadium . A match to do things well, to suffer and take advantage of the details that have gone against us in previous matches and not today. I am very happy for my players, they have made a tremendous effort.
"A lot of people from Pamplona came who believed in us and followed us from their homes. This is also for them.
"I don't know what the draw will bring, but we are in it. The possibility of fighting in the next round is a big deal. Being able to experience another night like tonight is incredible. I have told my players that we were playing against a great team, but that we are also great. We are a very difficult team to beat."