Everton were reduced to 10 men when 1-0 up but held on and even added a second goal deep into stoppage time, and Moyes was pleased with his players' efforts at both ends of the pitch.
"We have been good for the majority of the season. We have had one or two dips but that was more like us today," BBC Sport quotes Moyes as saying.
"I thought we played really well in the first half. We were playing the champions so we knew it was going to be tough.
"When we had to be resilient we were and when we had to play well, we did. We scored a goal which was wrongly disallowed. I'm really pleased with how the players performed."
The result lifted Everton above Merseyside rivals Liverpool into sixth.