The former England forward was fired on Tuesday after only 13 weeks in charge, following a terrible run of nine defeats in 15 games.
Rooney, 38, said 'it will take me some time to get over this setback' and plans to spend time with wife Coleen and their children as he looks for his next job.
In a statement, he said: 'I would like to thank Tom Wagner, Tom Brady and Garry Cook for the opportunity to manage Birmingham City FC and the support they all gave me during my short period with the club.
'Football is a results business - and I recognise they have not been at the level I wanted them to be. However, time is the most precious commodity a manager requires and I do not believe 13 weeks was sufficient to oversee the changes that were needed.
Wayne Rooney was sacked as Birmingham City manager on Tuesday following a poor run
Rooney said he plans to spend time with wife Coleen and children Kai, Klay, Kit and Cass
Since Rooney arrived, Birmingham have fallen from the play-off spots to a relegation battle
NFL legend Tom Brady (left) is one of Birmingham's minority owners after the club was taken over by Tom Wagner's Knighthead Group in July
'Personally, it will take me some time to get over this setback. I have been involved in professional football, as either a player or manager, since I was 16.
'Now, I plan to take some time with my family as I prepare for the next opportunity in my journey as a manager.
'Finally, I wish Birmingham City FC and its owners my best wishes in the pursuit of their ambitions.'
Since Rooney replaced John Eustace in October, Birmingham have had the worst record in the Championship. They took 10 points from a possible 45, losing nine and winning just two.
The futures of fellow staff members Ashley Cole, John O'Shea, and Pete Shuttleworth were being resolved on Tuesday morning.
The decision to appoint Rooney will surely go down as one of the worst in the history of the club.
When he was appointed in October to replace Eustace, Birmingham were sixth. He leaves with Blues only six points above the relegation zone and with the worst record in the division during that time.
Rooney is unveiled as Birmingham's new manager on October 12 - but his tenure is now over
John Eustace was replaced by Rooney despite Blues sitting in the Championship play-off spots
Mail Sport understands Eustace would be open to returning to Birmingham but it seems highly unlikely that they would choose to reappoint him after already being forced into a such humiliating climbdown over Rooney.
This was Rooney 's third job in management. After spells with Derby in the Championship and DC United in Major League Soccer, he was brought back to England charged with bringing a 'no-fear' football philosophy to Birmingham.
Blues were taken over by an American consortium Knighthead last summer, a group of which NFL great Tom Brady is also a part.
But the Rooney experiment has been hugely embarrassing from start to finish and the credibility of the new owners will rest on what they do next.
Rooney's long-term future in management now appears unclear.