The Magpies fought back from two goals down at St James' Park to earn a share of the spoils in the Premier League encounter.
Despite being at the bottom of the table with just three points from five games, Williamson believes that Saturday's result is a good example of the spirit within the Newcastle camp.
"I think we showed the togetherness which exists within the squad with that result," the 30-year-old told the Daily Star. "It was a tough afternoon for all of us but we showed character, resilience and what it meant to the lads to come back."
Newcastle are back in action tonight when they travel to Crystal Palace in the third round of the League Cup.