Former Celtic frontman Gary Hooper fired the hosts into the lead at their Colney Training Ground before Jamaica international Jamal Loza doubled their advantage.
Foxes ‘keeper John Maddison then denied Jacob Murphy and Hooper in quick succession with Steve Beaglehole’s men coming back into the game.
A much-improved second half display saw City midfielder Jak McCourt curl a free kick just wide on the hour mark.
But Loza, who looked a threat all game, scored his second on 78 minutes before rounding off his hat trick after cutting in from the wing.
Substitute Cameron McGeehan, who replaced first teamer Jonny Howson on 61 minutes, scored the Canaries’ fifth of the game to round off a disappointing afternoon for the young Foxes.
In search for their first win of the Premier League season, City next host Chelsea on Saturday 27 September.