The Pittodrie side were well and truly outclassed in San Sebastian.
Sociedad should have been out of sight after dominating their visitors completely. However, the Spaniards could only chalk up a 2-0 first leg lead which leaves Aberdeen with a slender chance of qualifying for the play-off round.
Despite the strength of the home side, Anderson performed convincingly at the heart of the Aberdeen defence alongside Mark Reynolds. The 35-year-old showed similar strength of character when he refused to give up hope ahead of the second leg at Pittodrie.
"We are quietly confident. We are not going to shoot our mouths off, we never do," said Anderson. "It would be disrespectful and a bit stupid to say we will get through to the next round. We will pick the bones out of it and hopefully we can capitalise on some things next week.
"I know they will feel they could have scored a couple more and it was a big step up from the previous game for us. We will learn from this and we are still in it.
"Things are going to have to go our way next week. It is only half-time and if we can get a good start next week then you never know.
"They are a very good team. They played Champions League last season and that speaks for itself. They will be one of the better teams in this competition. I thought they were what you would expect from a team playing at the top end of the Spanish league.
"They were comfortable on the ball, but in saying that we limited them to very few clear-cut chances and I don't think Jamie Langfield [the Aberdeen goalkeeper] has had too many saves to make. It was always our plan not to be too open and to give them space to play.
"It worked well to an extent but after the first goal went in the game changed. The pressure was off them and you could see them play with a bit more freedom in the second half.
"It is a long 90 minutes against a team like that. I think if we had retained possession of the ball a bit more it might have helped us a little bit more when it came to stop their flow of play. We were disciplined in the defence side of our game, which we had to be, but the disappointing thing is we didn't retain possession and we didn't get up the field and at them. That is something we will need to address."
Anderson is hopeful the Aberdeen supporters can help the Scottish side to achieve what would be one of their finest nights in Europe. "We need to get the Aberdeen fans behind us to make it as intimidating as possible," he said. "They are experienced players and will be used to that but if we can get the fans behind us then it will help us take the game to them. Hopefully, if we can score a goal then it will give us the spring to really kick on."
Anderson had been instructed to mark Alfred Finnbogason in Spain, a long-term target for Celtic but an £8m summer signing for Sociedad. "It shows the difference in finances from a club like Sociedad and Aberdeen, but we can compete and that is what we hope to do next week," the defender added.
"He led the line well and was busy. Their movement, not only him, alongside their other forward players made it difficult."