Williams was one of the stand-out performers in Swansea's 3-0 derby triumph over rivals Cardiff City on Saturday, a fixture that marked Monk's first game in charge following the departure of Michael Laudrup last week.
After Wayne Routledge opened the scoring at the Liberty Stadium, Williams sprinted to the touchline to embrace Monk - who he has partnered on several occasions at the centre of Swansea's defence.
And Monk waxed lyrical about his skipper, saying. "What a top guy, what a captain as well.
"I played with him so many times. I know what it means to him. This club means a lot to him. It means a lot to a lot of those players in there.
"I think the newer boys, that will show them as well. They believe in the club.
"Ash has got standards. He's a fighter. At times I have had to try and tell him that he just has to worry about himself because sometimes when he gets too het up it affects his performance.
"He needs to worry about himself. You could see how much it meant to him and everyone else. It was amazing, brilliant."
