Mourinho blames Del Bosque for Costa problems
Costa has not played since featuring twice for his country in Euro 2016 qualifiers against Slovakia and Luxembourg, suffering from a hamstring complaint and a virus.
Mourinho says the latter issue has now cleared up, but claims it hampered the striker's recovery from injury.
"The virus is fine," he said. "It was hard, he had to go to the hospital and obviously it doesn't help him to recover from his injury. But he didn't play on Sunday because of the injury, not because of the virus.
"Diego has the hamstring [injury] because he played two matches in three days when he was not with us."
Questioned whether he hoped Costa's fitness problems were over, Mourinho quipped: "But he still has [to play for] the national team in November!"
Chelsea face League Two outfit Shrewsbury Town in the League Cup on Tuesday, with Costa unlikely to feature, but Mourinho insists he is not taking the fourth-round fixture lightly.
"You can say that Shrewsbury in the Capital One Cup is a friendly, but we have to play the match and respect the match," Mourinho added.
"They are doing very well in their league, they did very well against superior teams [Norwich City, Blackpool and Leicester City) in the Capital One Cup.
"It is a big day for them and we know it is going to be difficult for us. And because we have so many injured players, it is even more difficult."