Tykes striker Davies blazed woefully over from the spot three minutes before his opposition namesake headed home the winner, leaving Hill's men with one win from 13 games and without a home success since September 1. Jonathan Greening's goal had brought the Yorkshire side level seven minutes prior to half-time following Blues' opener, which came against the run of play.
"We would have been 2-1 to the advantage but we've got to accept that he (Craig Davies) has made the wrong decision. He's scored penalties for us, important goals and today he's missed a penalty so I accept there're vulnerabilities to everybody," Hill said.
"We have to take it don't we? It's a measure of the task that we've got. We look as though we're controlling a football match and maybe shoot ourselves in the foot - not once but twice, three times - the penalty as well, that's football.
"To be perfectly honest, the first goal I think it's a really good cross in. I think he's got between players and the goalkeeper.
"I think we've got to have a bit more assertiveness so I'm not going to lay blame, but the second goal, players have taken their own responsibility to change markers.
"Now it's not their responsibility to change who I allocate to mark at corners and set-plays and that's where we've been done."
Birmingham manager Lee Clark named five teenagers in his starting line-up and praised their performances as they helped the side to a first win in four.
He said: "The last two games we've had, the four points we've taken and the manner that we've done it in is great credit to the young boys - that was quite an old team for us now; five teenagers in the starting 11.
"What they're doing is showing great spirit and enthusiasm. They're talented footballers, you would like to put them in a couple at a time rather than drop them all in at once but they're producing individual performances and spirited collective performances, which is more important to get us positive results that mean they stay in the side."