A poor run of form in February and March saw Harry Redknapp’s side concede a 12-point advantage over their top four rivals as Arsenal leapfrogged them into third place.
Saturday’s point at the Stadium of Light has moved them back above the Gunners, with Arsene Wenger’s men due to host Manchester City on Sunday, but wins for both fifth-placed Chelsea and sixth-placed Newcastle United has seen that gap close to just three points.
However, Parker believes Spurs can only concentrate on their own fixtures, not those of their competitors.
He told Sky Sports: “It gets to that point in the season doesn’t it at the end of the day we have to concentrate on what we can do we need to go and win as many games as we can, six games left we need to keep picking up points and continuing that way.
“I think at the end of the day you have to worry about yourselves, if we win our games we’re fine. We know how good this league is.
“Newcastle have done fantastic along with Chelsea and Arsenal that are chancing they place so it’s all to play for but I think it’s in our hands and that’s where you want it to be. “
The former West Ham United player admitted it was a frustrating afternoon as the Black Cats defended in numbers to stifle the visitors.
He added: “It was quite a slow game out there. We dominated possession especially first-half and even second-half I think it was down to the way Sunderland set-up they got behind the ball and let us have it.
“It proved to be a difficult afternoon we couldn’t really get the goal we were searching for but we’ll take a 0-0 and go back and get ready for the game on Monday.
“I think we were a bit surprised by the way they set up, we probably expected them to come at us a bit more which obviously they didn’t. We’re disappointed we haven’t got the three points but we’ll take a draw a move on.”