The Basque club, who have been weakened by a need to cash in on a number of their best players in recent years, had a poor start to their La Liga campaign before stabilising under Moyes after he replaced the sacked Jagoba Arrasate last month.
When they return after the two-week winter break they host second-placed Barcelona at their Anoeta stadium in San Sebastian and the Scot said their first five or six matches in 2015 would be crucial to their chances of moving up the table from their current position of 14th.
Sociedad finished fourth in 2012-13 and qualified for the Champions League group stage, where they finished bottom of their pool.
Last season, they were seventh and secured a place in Europa League qualifying but were eliminated by Russian side FK Krasnodar.
"It is going to be difficult to get back into Europe, we all have to be clear about that," Moyes said in an interview published in As sports daily on Tuesday.
"Right now I am focused, and this is my obsession, on winning all the games we can so that we can make sure of avoiding relegation as soon as possible," the former Manchester United and Everton manager added.
"If we get some good results at the start of the year we can start to look up at the places above us."
Moyes said he was enjoying living in Spain and his biggest challenge was learning the language.
"I am learning words mainly to do with football which are helping me with my relationships with the players," he added.
"I have given myself time to get to know the players better, the club and everything around it, and my picture is already more complete.
"Everything we want to change in the future has to be done gradually and not in a drastic way.
"We will change things but in a logical way. In any case, the only thing that matters to me is that the team moves up the table step by step."
(Writing by Iain Rogers; Editing by John O'Brien)
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