The former Manchester United hitman has now lost six of his nine games in charge since replacing John Eustace at St Andrew's.
O'Hare had not scored for more than 18 months after suffering a serious knee injury on Boxing Day last year and was starting just his second game since returning from injury.
The 25-year-old opened the scoring after he was played in by Milan van Ewijk, before his superb solo goal made the three points safe in the second half.
"I thought we started the game quite brightly, but our decision-making wasn't the best," admitted Rooney.
"It was something we've been working on, playing in the opposition's half and trying to create better chances.
"The first goal is poor from our point of view. I felt like we were still in the game, we were trying to get an equaliser and they get the second goal from our corner.
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