Laura C. answered 11/13/20
Laura Teaches-You Learn
First, let us set the scene of this speech. It is one of despair, wherein the king comments on the hundreds of deaths that have taken place, "All murder'd..." the king proclaims. "...for within the hollow crown...keeps death his court..." and so forth. Here, he questions the reason for the deaths, for he too is mortal. From this monolog we see the guilt of the inner man. Which now separates him from the monarch, which is the outer man.
The "Cover your heads" is a reference to the deference and reverence one paid to a king. They would uncover their heads when in his presence, out of respect. The king tells them to do away with the reverence they pay him. Indeed, a few words later comes the meaning, when the king utters this, "throw away respect..."
I interpret this as Richard feeling absolutely undeserving.