Birmingham parted company with former Tottenham and West Ham boss Redknapp after slumping to a 3-1 defeat at home to Preston, one which leaves them 23rd in the Championship table.
It was their sixth loss in succession and sees the end of a tenure which began late last season.
Redknapp came in to save the Blues from relegation and achieved that goal with two wins in three matches, before signing a one-year deal to stay at the club.
Despite signing 14 players during the summer transfer window, Birmingham have managed just one win from six games this time around.
Former Blues midfielder Carsley has been appointed as caretaker-manager
"Maybe not this year but over the next two years I would have got promotion," a disappointed Redknapp told the Birmingham Mail.
"I had to do well this year but I would have stayed because I loved it there, absolutely loved my time there.
"I am not an idiot, I am not a silly person who goes around saying things, I think I have been around long enough."