Apart from striker Morata, the club's record signing from Real Madrid, new boys Antonio Rudiger, Davide Zappacosta and Tiemoue Bakayoko also featured against the Foxes.
The Spanish striker and Chelsea asked supporters to stop chanting the offensive song.
'We all know very well the importance of this player (Hazard) for us, ' the Italian manager said of the 2015 PFA Player of the Year.
PFA Player of the Year Kante was instrumental in the Blues' title win last season, while Drinkwater could make his debut after arriving at Stamford Bridge on deadline day. Alvaro Morata has told Chelsea supporters to "respect everyone" after the club condemned a song about the Spaniard that includes an anti-Semitic slur.
"This is good news for us, " Conte said after his side's third straight Premier League victory. We were in total control and could have scored more goals.
"But if he scores, I am very happy". Conte, as quoted on Chelsea's official website, called him a fantastic player and insisted he had an wonderful game. "He made good runs with quality and he is improving a lot his passes and finishing".
Fortunately Hazard has returned to Cobham unscathed and it is to be seen whether Conte would deem the Leicester match important enough to risk aggravating his injury.
Conte's men were in control from the off and had the game wrapped up when N'Golo Kante added to Morata's opener on 50 minutes.
"We were in a good position at 2-0 but suffered to the end".