Daniel 3:16 (ESV)

16 Shadrach, Meshach, and Abednego answered and said to the king, “O Nebuchadnezzar, we have no need to answer you in this matter.

The response of the three friends is based on faith, on their bond of love for the Lord. They are not ashamed of him. They say that it is not actually necessary for them to answer the king, because he knows that they serve only the Lord, the God of heaven. He knows that they are not at all inclined to give divine honour to state power, to an image. They do add something to their answer (see next verse).