Mourinho spoke out on Friday after Lukaku suggested he was forced to temporarily leave Chelsea for Goodison Park in the close-season, with the Portuguese refuting those accusations by indicating the forward was the driving force behind the switch.
And Martinez - who watched Lukaku score his eighth Premier League goal of the season in his side's 4-0 thrashing of Stoke City on Saturday - feels Mourinho is within his rights to talk about the Belgian.
"I hate when there are comments about our players but this is not the case," the Spaniard said.
"We have got a player on loan and the parent club is entitled to say whatever they want about their relationship with the player."
Former Wigan Athletic boss Martinez went on to laud Lukaku as a "true ambassador" for his parent club.
"It is important to see that Chelsea wanted Romelu to get some playing time and allow the player to develop and that's happening," he added.
"The relationship with the player is working extremely well. (He's) scoring goals, he's working hard - he's a true ambassador for Chelsea football club and we're just enjoying having the player around."
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