Yes, these two phrases have the same meaning. They are both correct as well. However, it is probably more common to say "My eyes were closed." For example, "I didn't see you walk in the room, my eyes were closed." It is correct and means the same thing to say, "I didn't see you walk in the room, I had my eyes closed." Both are good!

These two sentences are written in different Voices: Passive and Active. I had my eyes closed - Passive Voice (Past Perfect Tense) My eyes were closed - Active Voice (Past Simple Tense)

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İlkinde ( I had my eyes closed) ; Bir zorlama anlamı var.Yani sen fiziksel olarak gözlerini kapayamıyorsun gibi ,"Gözlerimi kapattırdım" tam çevirisi olur. İkincisinde (My eyes were closed) ; "Gözlerim kapalıydı" Burada sadece cümlenin geçtiği zamanda sadece kişinin gözlerinin kapalı olduğu bilgisi çıkıyor.