Coleman's two-year contract extension, which will run through the 2016 European Championship qualifying campaign, was confirmed by the Football Association of Wales on Friday.
The deal was not met with the universal approval of the Wales' supporters, but Williams and his team-mates are glad to see the former Fulham boss stay on as they prepare to face Finland in Cardiff on Saturday evening.
"It was almost like we took it for granted he would be in charge. None of the boys or the manager have said anything any other way," said Williams.
"We just thought he would be the manager, we came in to the camp and it was business as usual, it was no different."
And the Swansea defender has called on the Wales fans to give their full backing to the team and their manager.
He said: "The negativity is not going to help at all, no matter what people think of him.
"The players all like him which has to stand for something and now he has definitely got the job so there is no point moaning.
"We all need to pull in the same direction, we need the fans right behind us and we all need to stick together.
"We want to qualify for the next major tournament and that has to be our goal and we have to tunnel vision towards that."
In stark contrast to the injury-ravaged squad that beat Macedonia and drew in Belgium last month, Coleman has Gareth Bale, Aaron Ramsey, Joe Allen and Williams all available.
Coleman has rarely been able to field his best side during his 14-game reign, and his captain knows Wales must start to make full use of their star talents and need to start delivering results.
He said: "We do not have any excuses, it is time for us to deliver," he said.
"It is a fact we have not been able to put out what people would say is our strongest XI and we need to do that as often as we can to perform as we need to.
"We were doing well a couple of years ago and then with the change of manager it took a while (to adjust), but you can see we are more consistent now and we are working towards good performances and results in every game.
"We have time before the next qualifiers but the general feeling is getting better and on Saturday we need to put a performance in, show what we have been working on and build on the last two performances."