The Tykes conceded twice from corners and, although they replied through Jacob Mellis with a quarter of an hour left, could not haul in the Bluebirds and force a draw.
"Everything is marginal, they are top of the league and we are near the bottom," said Hill afterwards.
"We have let (goalkeeper) Luke Steele down. He has made two matchwinning saves and we conceded from both corners and the players are responsible for the individual mistakes they have made.
"The individual errors cost you and that is the difference between the cream and the elite and us at this moment in time. Performance-wise there wasn't an awful lot of difference between the two sides. But that is the mentality of winning.
"It is the first time we have conceded from set-plays in a while and we have conceded two. That's what has cost us. We huffed and puffed, we could have had one or two decisions go our way, but we didn't get them. But we need to show more ruthlessness to make sure the opposition don't score."
Ben Nugent and Aron Gunnarsson were the men to benefit from some generous marking from the hosts as Malky Mackay's side went top of the Championship.