Chris Wood netted a first-half treble and Matty James completed an emphatic victory with a well-struck shot after 52 minutes.
The result leaves the Robins rock bottom of the npower Championship and McInnes was relieved of his duties shortly after the match.
Straight after the game he said: "A lot of players let the fans down in the first half.
"The first three goals were self-inflicted. Dean Gerken would say himself that he didn't have the best of games, but there were errors in front of him as well.
"We were too pedestrian in our play and made it easy for a very good Leicester team.
"The performances of Wes Burns and Bobby Reid gave everyone a lift. I thought seriously about starting Wes when Sam Baldock was ruled out by injury and he showed he has the temperament as well as the ability for Championship football."
- Sports & Recreation
- Matty James
- Dean Gerken