The Japanese midfielder has struggled for first-team starts this season for the Red Devils, but was crucial in his side's 1-0 victory in their Group A clash at Old Trafford.
"I thought he was really good," Moyes told reporters. "His effort when we didn't have the ball was fantastic. Everybody tells me [about] his abilities and what he's got and tonight (Wednesday) was the first time I had really seen Shinji.
"Shinji, I thought, played really well tonight. I thought when we put him into the number 10 role, even after he was very good with Wayne [Rooney], and off the left tonight. And he plays off the left for Japan.
"His attitude and his energy were excellent and I was pleased for Shinji. As I said, that was the best I had seen him play since I have taken over."
A second-minute own goal from Sociedad defender Inigo Martinez was enough for United to pick up the three points at home.