However, he did admit that his players fell away during the second half at the Riazor Stadium in rainy Galicia after dominating the opening 45 minutes.
Moyes, who was sacked last April after less than 10 months in charge of Manchester United, said: “I really enjoyed it.
“I thought we had done enough in the first half to be in the lead but we started the second half slowly and we gave away possession far too easily and too many times.?? ?? ?? ?? ?? ????
“I was disappointed with the second half. They were the better team in the second half but I thought we were the better team in the first.”
As for the challenge ahead, he added: “I don’t know the players well enough to give a comprehensive view on all of them yet.?? ?? ?? ?? ?? ????
“It will take some time but hopefully we can see some quick results and some improvement in the team over the coming months.?? ????
“Overall, I was really pleased with how the players went about it. I thought their attitude was very good tonight.??
“I wasn’t happy with just a point, I wanted to win. But in the end maybe a draw was a fair result.”??
After 12 matches, Sociedad are 14th in the 20-team table with 10 points having collected just two wins leaving them a single point above the relegation zone.
Moyes’??next game in charge will be at home against Elche on Friday night.
Watch Real Sociedad v Elche live on Sky Sports 5, kick-off 7.45pm on Friday evening.