Lukaku scored the third goal in the 4-1 defeat of a Malaysia XI in Kuala Lumpur for his second goal of the club's pre-season tour of Asia.
In the absence of Fernando Torres, who is on holiday following the Confederations Cup, and with Manchester United clinging on to Wayne Rooney, Lukaku is bidding to take his Blues opportunity after a successful loan spell at West Brom.
But despite the Belgian sharing similar traits to Ivory Coast forward Drogba, who was a key member of Mourinho's squad first time around and who scored the Champions League-winning penalty in 2012 before leaving Stamford Bridge, the Chelsea boss was not prepared to make a direct comparison.
"We have to respect Didier, because Didier's unique in Chelsea history," Mourinho said.
"And we have to respect Lukaku and the best way to respect Lukaku is not to compare him with a legend of Chelsea Football Club.
"The kid is good."
Another player keen to do well is Bertrand Traore, who is a 17-year-old Burkina Faso international, in his second six-week trial spell at Chelsea.
After impressing academy coaches in 2012, Mourinho watched a DVD of the athletic midfielder before inviting him to the Asia tour.
As he is not 18 until December, Chelsea and Traore must wait to sign a permanent deal.
Mourinho added: "Now we want to keep him. We have to wait until he becomes 18 to try to get a permit for him to stay in England.
"It's the rules and we have to accept them."
Mourinho hopes forward Kevin de Bruyne's knee injury is not serious after the Belgian was injured in the act of scoring the second goal of the victory at the Shah Alam Stadium.
Mourinho said: "When he was on the floor and asking for a change, everybody on the bench, we thought the worst.
"The first assessment by the doctor was that it was not the ligaments for sure and if it is something in the meniscus, then it has to be a very small injury.
"So we believe it is not an important injury and hopefully it isn't because the kid is a fantastic player and is showing to you match after match and showing to me in training that he is going to be a key man on the pitch."