Barry scored the only goal of the game on the hour mark as Everton won 1-0 on Sunday.
Moyes said afterwards: "I always hoped (Barry) would come through. I don't think it's easy as a young player coming from overseas to the Premier League. Thierno has the even more difficult one of being a centre forward trying to score goals.
"I think we're going to have to give him time – there are lots of things that he needs to improve on greatly, so we're not getting carried away but he gets the winning goal today and if you do that in games, which is important, it means an awful lot.
"Then I think that Evertonians might have just started to see a bit more of Merlin Röhl today. I see quite a lot of it in training. He's been up and down a little bit and he's coming back from a hernia operation, so he's just beginning to get an idea of what the Premier League is like.
"He's got loads to improve on as well but if we're going to judge them so quickly then we're not going to give them an opportunity (to show their best).
"I say it because the people who have watched Everton for many years will know the likes of Leighton Baines, Joleon Lescott, Phil Jagielka – they all had to bide their time before they got regular games. I'm not saying it's exactly the same but if they go on to be as good as any of those players, that's what we want."