Richards has praised his former boss, who led the club to FA Cup glory in 2011 and a Premier League title win in 2012.
"Mancini did fantastic in the three years he was here," said Richards.
"The owners have decided they wanted a change and that was up to them but I'd like to thank Mancini for what he did for me.
"Winning the Premier League, FA Cup and Community Shield was brilliant, I'd never won anything before.
"I'm happy for that but we are moving forward now, and looking forward to whoever it is going to be (who takes charge) and seeing their plans."