The former England and Manchester United captain succeeded John Eustace as Blues boss earlier this month.
Eustace, 43, was sacked following back-to-back wins that had seen Birmingham climb to sixth in the Championship table.
Rooney has since overseen two losses out of two, with Blues falling to 12th.
He lost his first game in charge 1-0 at Middlesbrough, managed by former Old Trafford pal Michael Carrick, thanks to Morgan Rogers’ 88th minute goal.
Last night Rooney took charge of his first home game as Birmingham boss, coming up against Hull.
Blues’ opponents were managed by Liam Rosenior, Rooney’s assistant from his days at Derby.
Liam Delap gave the visitors a 12th minute lead at St Andrew’s, before Jaden Philogene doubled their advantage in the second half.
After the match, some disgruntled Birmingham fans let Rooney know of their displeasure.
According to ESPN’s Mark Ogden, one even told him to “f*** off back to America” as he headed for the exit.
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Prior to joining Birmingham, Rooney had been managing DC United in MLS.
The 38-year-old managed just 14 wins out of 53 games in charge in Washington, drawing a further 14 and losing 25 – possessing a win percentage of 26.4 per cent.
He’d previously managed Derby during a period of financial difficulty, winning 24 out of 85 games in charge, at a percentage of 28.2 per cent.
After last night’s match, Rooney told the BBC: “There were some good moments but we created problems for ourselves, giving the ball away too cheaply.
“And the really disappointing thing was that, after the second goal, I didn’t see a response and I’ve told the players that.
“That last 10 minutes or so told me a lot. It was a concern for me and it’s something that won’t happen again.
“We have to be patient – and we will get there. At the minute, we’re on a learning curve.”
Rooney’s quest for his first points in charge of Birmingham will continue on Saturday, when his side travel to Southampton.
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