The context of Romans 8 is somewhat different than the context in Hebrews 8, but the principle Paul deals with is similar. Flesh in Romans 8:3 refers to people. The problem with the Old Covenant was not with its laws, but with one of the parties who made the covenant—"them" (Hebrews 8:8). Obviously, he refers to the people who made the covenant. They would not keep its terms!
This is confirmed by the Old Testament record, which shows that Israel never kept the Old Covenant except for brief periods of time. This is why there are so many references in the Old Testament to their being stiff-necked, being fornicators or adulterers, or filled with iniquity.
It was not that Israel could not keep the terms of the covenant but that they would not. God's intent in making the Old Covenant was limited. Israel should have been able to keep its terms. To think otherwise is to accuse God of being unfair in His proposition and having taken advantage of Israel's ignorance. Human nature is always looking for ways to shift blame.
We must be careful, or we might be guilty of doing the same thing under the New Covenant. We could say that it is too hard, and use our complaint as a justification for our failures and bad attitudes. Jesus anticipated this.
In the Parable of the Talents in Matthew 25, He gives five talents to one, two talents to another, and one talent to a third. The response of the person to whom He gave one talent is, "I knew that You were a hard man, and that You reap where you do not sow. And therefore I hid it" (Matthew 25:24-25). He is saying, "God, You were too hard!" He essentially shifts the blame to God. Jesus understood that human nature never changes: It always wants to shift the blame!