The Australian international handed Watford the lead late in the first half as his chested ball was well short of goalkeeper Jason Steele, allowing Matej Vydra to edge in and give the Hornets the advantage before eventually winning 2-1.
Williams has only recently returned from a lengthy spell on the sidelines with an ankle injury prompting Mowbray to let excuse him for the uncharacteristic error.
"I used to play football through fear of not making a mistake. Rhys has been out for four months and has only been back for four games. He has to get back into the swing of things," said Mowbray.