Rookie,
The OP asks "How should this be handled"? Do you mean the situation on the floor or how it should be handled now that it's over.
On the floor, you can't go back. But these are lessons that stay with us. Late in the game, all officials have to be on top of such things.
If it was me, I would apologize to the coach; probably through my assignor. Some may not agree with this but I believe that coaches appreciate that officials are capable of admitting a mistake. The coach wrote a letter that was reasonable; he did not ask for heads to roll. A reasonable response from the assignor or association would be appropriate.
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