The former Real Madrid fullback, now 29, was emotional as it was his first goal in four years after an extended period of injury problems.
Odriozola said afterwards: "I'm so proud, I won't lie. I'm coming off a very difficult period, I had a really hard time. I wasn't able to help the team of my life.
"I'm very hard on myself, I wasn't able to defend the crest as much as I would have liked. My body didn't respond, it wasn't in tune with my head."
The 29-year-old then went into detail: "A month ago I had a turning point. I was close to leaving, I wanted to play, I wanted to be myself again. Playing today and scoring... I was in hell. Nothing worked for me. It's so painful. I'm privileged to be at the club of my life.
"I'm the father of two little girls, the goal is for them and for my girlfriend. But I'm not leaving happy because we didn't win."
He also said: "These are emotions you can't control. When you give everything and then you get repaid... It's been a really tough time, because I'm at home. All my loved ones are Real Sociedad fans. People are suffering, and we are human too. I don't know if I'll play again, but the next day I'll train and give everything to Zubieta.
"My dream is for my daughters to see me run at Anoeta. I support Real Sociedad with all my heart, even if there are those who don't believe it ."