Moyes took over at Sociedad in November after the Basque club made a shocking start to their 2014-15 La Liga campaign and the former Everton and Manchester United manager led them to a creditable 12th-place finish.
The Scot is clearly anxious to take the San Sebastian-based side to the next level but their only real signing of note since the end of last term has been Brazilian forward Jonathas from relegated Elche.
"I don't think that right now we have to have Europe as a goal," Moyes told a news conference on Friday ahead of the La Liga opener at Deportivo La Coruna (1630 GMT) on Saturday.
"Considering what we did last season, looking to Europe is a very big step," added the 52-year-old.
"I hope we can do it but I don't think we have to have that expectation from the start."
Moyes said he was "satisfied" with the new players who have arrived but coaches always wanted more.
He gave little away when asked about reports suggesting Sociedad may strike a deal to take their former midfielder Asier Illarramendi on loan from Real Madrid.
Illarramendi, 25, moved to the Spanish capital two years ago but has been unable to hold down a regular place in the starting lineup.
"If a midfielder we believe can help us was available I am sure the president would be interested," Moyes said.
"But I am happy with the midfielders we have and there is competition for all the positions, which means the players have to perform very well to win a place in the team."
(Reporting by Iain Rogers, editing by Ed Osmond)
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