Barry struck a first goal for the club as Everton won 3-0 at Hill Dickinson stadium.
Moyes said afterwards: "We’ve won four out of five, with one disappointment in there but, overall, we’ve got the win, we’ve got the goals and I think, more importantly, we’ve got the clean sheets.
"If we're going to be any way successful, whether that be whatever part of the league it is, we're going to have to get clean sheets and we've suddenly started to get a few now, which is really pleasing."
On Barry, he stated: "I think the crowd have recognised there's an improvement. They think he's got close. I have to say, I have to give huge praise to Ili Ndiaye for the weight of his pass. It allowed (Barry) to walk onto it and stroke home at one touch. He couldn't have put it any more perfect.
"It was really, really good play by Ili and obviously a really good finish with Thierno."
Moyes also had a word for the performance of Kieran Dewsbury-Hall.
"He's given us something else. We're having to play him a little bit lower at the moment and a bit deeper in the team because of the players we have missing. We picked up two wins on the bounce which is not easy in the Premier League at the moment.
"Even today, they had a chance at 2-0, which could have put us on the back foot and fighting. But we ended up with a great result for us."