Harry Redknapp's side has only won one of their last nine matches, a run which has seen them move from third to fifth in the table.
Their latest setback, a 1-0 defeat at QPR, saw them drop out of the top-four after being leapfrogged by Newcastle, who now hold a three-point lead over the London club.
"Of course we can turn things around," said the 31 year-old. "There are still four games to play, all winnable games if we perform to our capabilities.
"We were all disappointed after QPR. I felt we had a lot of the ball without creating too many clear-cut opportunities. We just needed a break and it was a tough one to take, losing."
Spurs take on relegation-threatened Blackburn Rovers on Sunday, and the club captain has called on his teammates to get the points they need to keep the pressure on Newcastle.
"We were all back into work on Monday, all looking towards Blackburn, trying to put a few things right and hopefully we can go on and get the points we need," added the Englishman.
King has admitted that he is unsure why Tottenham haven't been getting results, as he believes that their performances haven't been particularly disappointing.
However, he has called on the players to remain positive and give it their all in the final four fixtures.
"We have to pick ourselves up. We can't feel sorry for ourselves. We've four games left and we have to give the best we can in those games and hopefully get the points we need," he continued.
Newcastle faces two of the top six teams in their four remaining games, playing Wigan, Chelsea, Manchester City and Everton.
Meanwhile, Redknapp's side will take hope from the fact that they face three of the bottom six in their remaining four games, playing Blackburn, Bolton, Aston Villa and Fulham as they hope to earn themselves Champions League football next season.