Goals from Steven Pienaar, Marouane Fellaini and Nikica Jelavic saw the Toffees follow up Monday's win over Manchester United in style. Villa could only manage a late consolation from Karim El Ahmadi as they lost their second successive match. To add to Villa's misery, defender Ciaran Clark was sent off for a professional foul on Jelavic after 58 minutes.
Moyes said: "We have won two out of two. We've always been good finishers to a season, and we've just got to make sure it doesn't happen in reverse. The job is to keep us going in the right direction. If you win two, it gets you off to an initial good start but you are judged a bit more after 10 games."
Moyes will look to strengthen his squad before the transfer window closes on Friday.
He said: "I'd like to add to the squad if we could just to make sure we've got enough bodies. If I can add a loan or something came up which we could manage, then I would look to do it."
Villa gave the appearance of a side which needs to be strengthened before the transfer window closes.
Manager Paul Lambert did not disclose his plans but admitted: "[Owner] Randy Lerner, myself and [chief executive] Paul Faulkner will sit and see what's going to happen.
"If something comes available and I think it's worthwhile, then you can look at it."
Villa, who won only four home games last season, were always chasing the game after Everton's early strikes.
Lambert said: "I was really disappointed. You can't in any game of football give someone a couple of goals start, particularly a team like Everton. You can't do it. The only pleasing thing was the second half - we kept going, which was pleasing, but the horse has bolted."
Source: PA
Source: PA