Everton managed to beat their rivals 2-0, following goals by Tim Cahill and Mikel Arteta.
Moyes told Sky Sports: “Their attitude was spot on and they got their reward.
“I thought we have played better in the majority of games than we did today but it was a derby and a different kind of game.
“Some of our performances (earlier in the season) were good but we did not get the result but today we did enough.
“We are getting away from the wrong end of the table. We are a good enough team to be at the top end.”
