Romelu Lukaku scored twice, and Dries Mertens and Michy Batshuayi grabbed a goal each as Belgium breezed past their Central American opponents on Monday night.
Speaking after the game, Ramirez claimed he didn't know the forward who grabbed the assist for Mertens' opener in the 31st minute.
He told reporters: "The 10 did us a lot of damage... I don't know his name."
Costa Rica's group opener is against Serbia on June 17, but the 53-year-old claims to have a plan for his side's first game in Russia.
Hazard limped off in the 70th minute with a dead leg, but head coach Roberto Martinez insists it's only a minor knock.
"Eden is OK; he had a little trouble, but it’s nothing to worry about," he said.
"I really enjoyed his performance. He was sharp and strong, he was majestic. At the end he just came off because he had a little bit of a dead leg; a little bit of a knock on his leg."
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