The 70-year-old was dismissed by the Midlands side yesterday after claiming just one win from the first eight Championship games of the season.
The former West Ham United, Portsmouth and Tottenham Hotspur boss had been in charge at St Andrew's for just four months, having helped them to safety on the final day of last season and overseeing a summer transfer window that saw 14 new players join the side.
"I have enjoyed my time there, I thought the fans were absolutely incredible people. It is a smashing club, there's nothing I would like to see more than them get back in the Premier League," Redknapp told the Birmingham Mail.
"I loved it there, the fans were great to me, absolutely fantastic, I enjoyed my time there.
"I wish the club going forward every success. I am not a bitter person. I don't go away and think 'Oh I hope they don't do any good'. I am not like that.
"I loved Tottenham, I love to see Tottenham doing well, love to see West Ham picking up again and doing well, I would love to see Portsmouth get back up the league and I would love to see Birmingham do well."
Birmingham are currently 23rd in the Championship table with a tally of just four points.