Spurs were frustrated by Martin O’Neill’s side who sat deep, allowing the visitors to have plenty of possession but suffocating any meaningful attacks.
And in a match lacking in goalmouth action, both sides had appeals for penalties turned down by referee Chris Foy, including a handball by Parker, though none were clear cut.
A point sees Tottenham climb into third above Arsenal, who host Manchester City on Sunday, but Parker knows it is up to Spurs to focus on themselves rather than the results of teams around them.
“It’s got to that point in the season where we need to concentrate on what we can do and we need to pick up points and keep going,” he said.
“At the end of the day we just have to worry about ourselves. It’s all to play for but it’s in our hands and that’s the way it should be.
“It was quite a slow game. We dominated possession but Sunderland set up behind the ball and let us have it.
“We were surprised by the way they played. We expected them to come at us a bit more but we will take the draw and move on.”
Spurs dictated the opening stages, with their midfield trio of Parker, Luka Modrić and Sandro controlling the tempo of the game.
But, an early Benoît Assou-Ekotto shot aside, Spurs created little and Sunderland began to creep forward hoping to capitalise from Sebastian Larsson’s set piece delivery.
Sandro was guilty of some defensive errors that almost let the Black Cats in, but neither side truly tested the opposition keeper.
The game improved after the break, and Gareth Bale should have done better than head over when completely unmarked.
Phil Bardsley offered a glimpse of goal for Sunderland, but his 20-yard drive was comfortably held by Brad Friedel.
As the game petered out, Martin O’Neill denied that he had told his team to play for the draw.
“Any frustration Spurs felt is part of football. We didn’t want to allow them to come here and just pick up the three points, it’s not like that,” he said.
“We were up against a side at the top of the league who have been vying for Champions League football and up until a few weeks ago had a chance to win the league.
“We have been frustrated here against teams but in fairness we had chances in the game, though we may not have hit the heights of last week.
“We have played two teams in the top four and got two points. We should have won at Manchester City last week and we got a draw here today. I have no complaints with that.”
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