Yes, mankind is under a curse. The curse is God's judgment.
Behold, I set before you this day a blessing and a curse; A blessing, if ye obey the commandments of the LORD your God, which I command you this day: And a curse, if ye will not obey the commandments of the LORD your God, but turn aside out of the way which I command you this day, to go after other gods, which ye have not known. (Deuteronomy 11:26-28)
The curse of the LORD is in the house of the wicked: but he blesseth the habitation of the just. (Proverbs 3:33)
And it come to pass, when he heareth the words of this curse, that he bless himself in his heart, saying, I shall have peace, though I walk in the imagination of mine heart, to add drunkenness to thirst: The LORD will not spare him, but then the anger of the LORD and his jealousy shall smoke against that man, and all the curses that are written in this book shall lie upon him, and the LORD shall blot out his name from under heaven. And the LORD shall separate him unto evil out of all the tribes of Israel, according to all the curses of the covenant that are written in this book of the law: (Deuteronomy 29:19-21)
For as many as are of the works of the law are under the curse: for it is written, Cursed is every one that continueth not in all things which are written in the book of the law to do them. (Galatians 3:10)