"Was Arsenal a wake-up call? I think we know we are not quite there yet and the players were not getting too carried away although sometimes it is hard not to, especially with three away wins in a row," Barry told the Birmingham Post.
"The first half was a big lesson. We saw some of the best football seen at Villa Park for a long time but the way we responded was good.
"We sat down at half-time, thought about it and took the game to them. We pressed them and, in the end, they were waiting for the final whistle.
"In terms of that style of football, there is probably not a team in the country to touch Arsenal.
"We showed in the second half how to play them a bit better, we pressed them higher up the pitch and didn't give them the space they had in the first half. We were unlucky not to get the draw, which might have been a fair result.
"The fans were great. It is not often you lose and the fans are still singing, right to the end.
"They want us to be top-four material and that is a big aim for us. If we fall short, finishing in the top six will still be a great season."