Kante, who joined City from Caen for £5.6m in August 2015, was one of the top players of the 2015-16 season as his industrious displays from midfield were key to the Foxes winning a maiden Premier League title.
However, the France international will play his football at Stamford Bridge this campaign after joining the Blues in deal worth about £32m.
It is the second season in a row that Leicester have lost an influential midfielder after Esteban Cambiasso linked up with Olympiacos last year.
"Last season we lost Esteban Cambiasso and everybody was crying," Ranieri said after his side drew 1-1 with Celtic in a pre-season friendly.
"Now we are crying because we lost Kante. Don't worry. Football in Leicester will keep going."