Williamson has had to battle for his first-team place and in recent weeks he has been a regular starter.
The former Watford stopper insists he did not think about quitting, and said: "It is tough when you are not playing because as a professional that is all you want to do.
"So it was a matter of biding my time and remaining positive.
"The manager made it clear on the first day of pre-season there would be competition for places, and anybody who wanted to leave had the opportunity.
"I always felt if I worked hard then I would be ready when I had my opportunity and I always believed that opportunity would arise.
"It came in difficult circumstances at Everton, but we have done well collectively ever since.
"Every time I have the opportunity to play, I pride myself on clean sheets and defending first.
"It is no-nonsense stuff from me.
"I will always give 100 per cent and do everything I can to stop the opposition and then give the ball to the creative players and let them do their jobs.
"It is a statistic I am very proud of and one I hope the manager is aware of."
Williamson is a rare breed having battled his way up through all four divisions of English football, but he insists it has made him the player he is today.
"I would not have it any other way as it gave me a fantastic grounding," he said.
"I have met some incredible players, coaches and managers on the way and it makes me appreciate every second I am out on the pitch in a Newcastle shirt.
"I make sure I take nothing for granted for this fantastic club, the atmosphere, the fans, the passion - and that extends to off the pitch as well.
"There is a chance to reach out and help in the local community in a number of ways.
"I like to make sure I am very active in that and for me that is just as rewarding as what happens on the pitch."