Yes, woman was to blame.
But so was man.
And Satan. It was a group effort.
SATAN devised the temptation, causing them to be
disobedient.
EVE listened to Satan and followed through on the
temptation.
God had told ADAM the rules of the garden, giving
him a leadership position. He failed to communicate those rules effectively to
Eve and, since it appeared that he was standing right there when it all
happened, Adam failed to enforce the rule. He too willingly participated in the
fruit eating, sharing in the sin.
Who did God blame?
Every one of them: Eve, Lucifer and Adam. All of them suffered life-changing consequences.
No one party was totally to blame for sin entering
our world. Only God was innocent.