Pickford kept a clean sheet on Saturday afternoon as Sunderland picked up a welcome Premier League point against Burnley, but the Black Cats remain rooted to the bottom of the table, seven points behind 17th-placed Swansea City.
The England Under-21 international, however, has claimed that his team 'still believe' that they can survive in the top flight this season.
"We're just that little fraction away from getting the results that we need, we've got to just concentrate on ourselves, not look too much at the table, just keep working hard and it will click," Pickford told Chronicle Live.
"We had a few good chances missed but on the plus side, at least we're creating those chances. We couldn't convert them but we've got to keep strong and keep believing in ourselves."
Sunderland will return to league action with a trip to Watford after the international break on April 1.