"'Lord, you are righteous, but this day we are covered with shame - the men of Judah and people of Jerusalem and all Israel, both near and far, in all the countries where you have scattered us because of our unfaithfulness to you. O Lord, we and our kings, our princes and our fathers are covered with shame because we have sinned against you.'" NIV translation
Daniel goes on to acknowledge that God is right in His punishment of the people. He admits that there is not one who has obeyed His commands and so all deserve what they have gotten.
Our prayers should acknowledge the same fact that, on our own, we deserve death and separation from God.
"The Lord our God is merciful and forgiving, even though we have rebelled against him; we have not obeyed the Lord our God or kept the laws he gave us through his servants the prophets." NIV translation
As he confesses their disobedience, Daniel also praises God for His mercy. We must remember that mercy is the fact that God does not give us what we deserve for our sins.
"All Israel has transgressed your law and turned away, refusing to obey you. 'Therefore the curses and sworn judgments written in the Law of Moses, the servant of God, have been poured out on us, because we have sinned against you. You have fulfilled the words spoken against us and against our rulers by bringing upon us great disaster. Under the whole heaven nothing has ever been done like what has been done to Jerusalem.'" NIV translation
Daniel now speaks of God's just punishment and it seems like a contradiction to what he just prayed about the mercy of God but it is not. Daniel is speaking of the fact that God's people were taken into captivity and Jerusalem was destroyed. That was bad but it was not as bad as the prescribed penalty of death.
"'Just as it is written in the Law of Moses, all this disaster has come upon us, yet we have not sought the favor of the Lord our God by turning from our sins and giving attention to your truth. The Lord did not hesitate to bring the disaster upon us, for the Lord our God is righteous in everything he does; yet we have not obeyed him.'" NIV translation
Daniel continues his confession with the fact that, even after this judgment, the people have not turned to God. He says that the people have not repented and looked for the "favor of the Lord our God" which speaks of His forgiveness and restoration. We are reminded that God holds out this gift (grace) but we have to turn from the direction that we were headed in. Today, it seems like many speak of the grace of God but fail to mention that it must be preceded by a change in direction.