"It's his first exposure in English football, such a difference to what he's used to," Barry-Murphy said after the game.
"His first minutes for the club, I think in such a valuable environment because it'll give him a unique taste of what English football is about. It's great to see him adjust to that and get into the flow so quickly."
Barry-Murphy indicated that Kayky may be getting more outings for the youth team in the coming weeks, rather than earning any immediate senior call-ups, as he gets up to speed with the demands of City's style.
"Hopefully he'll be with us whenever the first team want us to use him," Barry-Murphy said.
"I imagine in the early stages of getting acclimatised to English football that will be pretty often. So whenever we get the chance to work with him that'll be great for us.
"He's made a great impression in terms of his personality and the way he is amongst the lads. Obviously, he gets to improve his understanding of the way we work and the language.
"The lads have gone out of their way to make him feel very comfortable and he seems very content and happy in what he's doing."