Williamson was the Magpies' fourth-choice centre-back at the start of the season but has impressed since coming on for the second half of the game against Everton at the end of September.
He has filled in for the injured Fabricio Coloccini and Steven Taylor and is confident he will keep his spot in the team even when the pair return.
Williamson admits it was hard when he was not playing regularly, although his family helped keep his spirits high.
"I'd be disappointed if I wasn't in the side at Spurs," said the defender in the Daily Star.
"It was difficult at times earlier this season. But life is about perspective. It's about having three children running you ragged so you have not got too much time to sulk.
"Now I'm playing I'd love to continue."
Williamson added: "Playing football is more of a rest. Away from the game, I try to switch off and that's not hard with my dogs and kids.
"On Thursday nights, I watch my boy play football in the pouring rain and I'm thinking, 'I've got to get home to cook dinner and then get to bed because I'm chasing Suarez on Saturday!'"
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