After the Belgian striker bagged a goal in the Blues' 4-1 preseason win over a Malaysia XI, the manager wanted to avoid putting on the pressure of comparisons to a club legend.
The youngster netted his second goal of preseason in Sunday's 4-1 victory, but the Blues boss does not want to put pressure on his charge's shoulders by putting him in the same bracket as the Ivorian, who scored 157 goals for the club.
Mourinho told reporters after the match: "We must respect Romelu and not compare him with Drogba as Drogba is a legend in this club.
"I am happy with his movement and he did what we asked of him. Steve Clarke did well with him at West Brom last year."
The former Real Madrid coach was also pleased with the rest of his team and its preseason preparations so far.
With Bertrand Traore, Kevin De Bruyne and Victor Moses also grabbing a goal each, Mourinho insisted that he was not interested with the result.
"I am happy with the preseason matches so far as we are able to apply what we did in training," he continued. "It was never about the result but more about the fitness and the performance of the players."