Although we can not keep up with God's standards on our own, God provided His righteous based on what Jesus gave. Considering that the plan of revealing God's righteousness is carried out by Jesus (and that all we do is receive it), Paul talks about the lack of boasting (especially on own merit).
Paul wrote that boasting "is excluded [...] by the law of faith" (3:27). Boasting is basically being able to show off what we did, but note that Jesus was the one who carried out the plan -- not us. The only part we have is receiving it by faith, and even then, it's in response God's outreach to us (as seen in Romans 3:10 -- note that John 12:32 talks about how Jesus draws everyone to Him, but Romans 3:10 can help explain why Jesus did so). So God not only provided the way to receive Jesus's righteousness but also showed us the way.
Hence, Paul concludes that "a man is justified by faith apart from the deeds of the law" (3:28). Justification by faith alone is one of the biggest parts of Christianity -- and a big distinction too. We are justified because of faith (which leads to receiving Jesus), not because of what we can do (partly because we can't accomplish all of God's law).