The national team coach alleviated the pressure following a disappointing start to World Cup 2014 qualification by guiding his side to a 2-1 victory over Scotland at Hampden Park
Coleman has come under pressure after a poor run of results in their quest to qualify for World Cup 2014 left them with just three points from their opening four matches.
Their win at Hampden Park, courtesy of goals from Aaron Ramsey and Hal Robson-Kanu, has boosted them to third place in Group A, however, Belgium and Croatia have raced ahead of the chasing pack.
"The manager was spot on against Scotland," Williams told reporters. "He made good substitutions and got all the big calls right.
"There has been criticism of him but not from anyone who matters. People have just been talking for talking's sake.
"We are not concerned about it and the lads are behind him. We enjoy playing for him, we enjoy the camps, we enjoy the training. Against Scotland you saw that he knows what he is doing."
Wales fell behind in the first half to a Grant Hanley goal and lost star player Gareth Bale to injury at half-time, but turned the game on its head after the sending off of Robert Snodgrass.
"It was a very important win for us," Williams added. "We need the points and there was a little bit extra riding on the game because it was against one of the Home Nations. It was massive.
"But we showed we can cope without Gareth. He dug in at Hampden and gave it a go but you could see he wasn't himself. He tried for 45 minutes but it wasn't right.
"But after that we came through and no one can say we are a one-man team. We were a goal down and came out for the second half without him. But we got the result and everyone played their part.
"That's the best I've seen from a Wales team. That is us at our best. That is how we want to play.
"We kept the ball well and didn't let Scotland settle on it. We won it back early and that is what we are supposed to do.
"We dropped off a bit towards the end of the half and they scored but in the second we controlled it pretty well. If we can play like we did for the first 25 minutes for a full game, we'll be a match for anyone."