Pienaar scored the first-half winner at Goodison Park as the Toffees clinched a home success to keep their hopes of securing a European place alive.
The hosts dominated for large chunks of the encounter and Moyes wishes they could have converted that authority into goals but was pleased to pick up three points and singled Pienaar out for praise.
He told Sky Sports: "I thought that we played well today and I thought that our football was excellent at times but we didn't really turn the good football into goals, which was required.
"While you're only winning 1-0 you're always worried about the counter-attack or them having a chance. They had one chance before half-time and we were grateful that it didn't go in.
"We couldn't get that second goal and because of that it kept it a little bit tight right to the end.
"We've dried up a little bit with our goals, which is a bit worrying because we've not scored enough. Our play has been good enough. But, nevertheless, the players have done very well in getting the three points today."
He added of Pienaar, who scored after a period of nice build-up play: "Steven played well today and gave us the creativity we needed.
"It was a brilliantly worked goal. It was a good football goal from our point of view. We felt we made good passes, played through and it was a good finish by Steven at the end."