"It was disappointing, especially with two first-half goals disallowed, the first was definitely onside," he said.
"The referee spoiled the game. They were giving me hits from behind and I was taking them but there didn't seem to be consistency.
"Sometimes that happens with the home team. We can't afford to let heads drop."
The Bluebirds have now lost four of their last five Championship matches and have dropped out of the play-off positions to ninth.
"It's a harsh league with loads of games coming thick and fast," Bothroyd told BBC Sport Wales.
"We need to gather ourselves and move on before the Derby game.
"If little things go your way you get the results but it's just not happening for us at the moment."