Costa has made a flying start to life in the Premier League since his close-season move from Atletico Madrid - scoring eight goals in six top-flight matches for Chelsea.
However, Mourinho warned recently that the Spain international was incapable of playing three games a week due to concerns over a hamstring injury that has dogged him in recent months.
Mourinho said in September that Costa was doing next to nothing in training due to the injury, but explained he was not caught off guard by Costa's inclusion in Vicente del Bosque's squad for European qualifiers against Slovakia and Luxembourg.
And the Portuguese warned he would not be resting Costa for Sunday's visit of Arsenal in order to benefit Spain's national team.
"My reaction to the news is no reaction because it's something I could imagine. It's not a surprise," he said on Friday.
"If he can play three in a week I think it's too much, but he's going to do that.
"I'm not going to save him to be in perfect condition for national team.
"He can play against Arsenal, he played in Lisbon, there are four days in between. He will be in OK condition for Arsenal.
"After that, during 15 days [in the international break] is not my responsibility."
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