Moyes was denied victory in his first Basque derby on Sunday when Sociedad let slip an early lead and drew 1-1 at home to Athletic Bilbao in La Liga.
The Scot said he was pleased with his team's first-half performance but was concerned by a drop in energy levels in the second period.
Bilbao were reduced to 10 men when Aymeric Laporte was sent off 10 minutes from time but Sociedad were unable to land a killer blow.
With 15 matches played, they are in 14th place on 14 points with Moyes having presided over one victory, two draws and a 4-0 defeat at Villarreal.
"There are a lot of things we want to improve, not just the physical part and the intensity but also the passing and the control of the game," Moyes told a news conference after the match at the Anoeta in San Sebastian.
"I think there were some good signs there, especially in the first half," added the former Manchester United and Everton manager.
"It was certainly an improvement on our performance at Villarreal and I think we have made a step ahead but we haven’t improved enough.
"I think the players are trying really, really hard to do so. The training has been great and I thought their attitude tonight was very good.
"I expected us to be stronger in the second half so that was a little disappointing.
"But we are in the middle of the season at the moment and we can’t change big things."
Moyes said he had enjoyed his first experience of the Basque derby and was looking forward to "a lot more".
He won three of the 24 Premier League derbies he took charge of, drawing seven and losing 14 against Liverpool and Manchester City.
Sociedad’s next outing is a King’s Cup last-32, second leg at home to third-tier Real Oviedo on Wednesday. The first leg at Oviedo, who are top of their group in Spain’s regional Segunda B, ended 0-0
(Reporting by Iain Rogers, editing by Patrick Johnston)
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