To add to lostwanderinsoul's post and answer Epic Bear Man:
It was always God's intention to put Adam, Eve and their descendants down on the Earth, He knew full well we would have shortcomings: We know this because the Qur'an says;
It is He who created for you all of that which is on the earth. Then He directed Himself to the heaven, [His being above all creation], and made them seven heavens, and He is Knowing of all things.
And [mention, O Muhammad], when your Lord said to the angels, "Indeed, I will make upon the earth a successive authority." They said, "Will You place upon it one who causes corruption therein and sheds blood, while we declare Your praise and sanctify You?" Allah said, "Indeed, I know that which you do not know." Qur'an 2:29-30
The lesson from the Story of Adam and Eve, may God be pleased with them, is do we repent and turn to God like they did, or do we become arrogant like Satan and blame everyone but Himself for his downfall?
Two paths, the gift of intelligence, reasoning and free will to decide for ourselves. Acknowledge we as humans are weak, we sin, we are far from perfect, but God is always there for us to turn back to.
Whilst we're on the account of Adam and Eve pbut:
God never blamed Adam's wife, Eve pbut for the sin that Adam pbuh committed. God spoke about both Adam pbuh and his wife being duped by Satan, and never singled the wife out. Adam pbuh is held responsible for the sin he committed, he cannot blame it on on his wife, since he is as a responsible human being as she. Both Adam pbuh and his wife were punished for their sin by being ousted from Paradise. The wife did not receive any harsher admonition than Adam pbuh and was not threatened by misery for herself and all her female offspring as depicted elsewhere.
Say, "Is it other than Allah I should desire as a lord while He is the Lord of all things? And every soul earns not [blame] except against itself, and no bearer of burdens will bear the burden of another. Then to your Lord is your return, and He will inform you concerning that over which you used to differ." Qur'an 6:164
This is also found in the Torah:
The soul that sinneth, it shall die. The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be upon him, and the wickedness of the wicked shall be upon him. Ezekiel 18:20