Iliman Ndiaye and James Garner struck the goals for Everton in the 2-0 win.
"It was everything we wished for,” Moyes told evertontv after the game. “We wanted a positive result today. We had a great atmosphere, a terrific new stadium.
“What I'm trying to do is hopefully give everybody a team which we can enjoy watching and be proud of.
“Today came close with their effort, their commitment. Some of the quality was very good, but there were other bits of it not so good. But, overall, really pleased with the result.
“(The atmosphere) was really good. I've got to say, we want to build on it. We have to build on it. We have to make sure that we've a stadium where, even when the game's a bit lulled, the supporters keep with us all the way.
“The atmosphere at the end of the game, as well, was immense because (the fans) probably realised how hard we had to work. We picked up a couple of knocks and injuries and different bits and pieces in the game. So that made it pretty difficult. We had to chop and change a little bit.”