The long-term future of the 35-year-old remains uncertain after he took over from Michael Laudrup in February.
The Swans clinched just their second win from 11 games in all competitions for Monk when they hit three goals past Norwich City.
"Maybe now people will stop judging every little thing, which is only natural and he's big enough to take that," The Mirror quotes Williams as saying.
"But, from our point of view, we've enjoyed working with him. We know that the best thing we can do for him is get results."
The Welsh outfit are seven points above the relegation zone in the Premier League table.