The Toffees welcomed back Moyes after 12 long years, as he took charge of the club for his second spell.
However, he was unable to help the team avoid a 1-0 home loss to Aston Villa.
“Obviously we're not pleased about losing but the game was very tight,” he told evertontv.
“We didn't have as many clear chances as them but we had opportunities. I think Jesper has a big chance to score with his head and Dominic has one at the end as well.
“If we’d got a goal, I don’t think anybody would have said we hadn’t deserved at least a draw but I can definitely see where the Club’s been now. We need some quality. I thought our quality on the ball tonight wasn't as good as it should have been.
“We couldn't make key passes to get us in control at the right moments or just give us the right opportunities. I thought we put two or three really good crosses in – Doucs had a chance with one in the first half. There were some really good things which we are pleased about but I can see now exactly what I’ve got.
“We were always in the game, we were never out of the game at any time. Obviously, what supporters are wanting to see is how are we going to get any more goals, where can we get the goals from. I’m not a magician, all I can do is try to look to see how we can find a way of getting goals. We've tried, we've encouraged the players to get forward more, we've encouraged them more to try to deliver good balls in, get in the right places to score.
“It's not for the want of trying. I'm just saying, maybe we're lacking bits of any areas of quality which might make us create more chances or score more goals or maybe create a pass which could get somebody in. I think that's quite clear to see.”