"We showed a lack of awareness defensively and they were crazy goals to give away," said Dave Jones.
"Our passing and movement wasn't right and there was no sustained pressure.
"We played at too slow a tempo and one or two heads dropped, so welcome to the real world.
"The two central defenders were done by simple through-balls but the full-backs and midfield players are also responsible.
"They can look at fatigue as a reason but we are better than that and never worked hard enough."
City's perilous financial situation means they are unable to bring any players into the club on loan.
"I cannot bring anyone in to change things around so we have to suffer it and work even harder," said Jones.
Tykes manager Mark Robins praised Bogdanovic's effort, which helped stop a poor run by his team.
"I always knew we were capable of winning matches, although we have been on a poor run lately," said Robins.
"I am pleased for the players and for the travelling support as we have taken them to the depths the last two away games.
"We knew we would have to defend as Cardiff have players who can score all over the field.
"Daniel Bogdanovic was excellent today and when he wants to compete he is a very intelligent player and it will be brilliant for the club if he continues like that."
