The White Hart Lane outfit have picked up just four points from their last four Premier League matches, a run that has seen Arsenal and Chelsea overtake them into the top four.
Fifth-placed Spurs narrowly missed out on Europe's elite competition last campaign after a slow finish to the season, but Dawson has stressed that a possible repeat is not weighing on the minds of the Lillywhites players.
"We're not thinking of that," he told Sky Sports News. "As players you can't. Who knows what will happen on May 19? Hopefully it will be a good day and we're celebrating. There's a lot of hard work to go in from ourselves and also the other teams to get there.
"Arsenal have gone above us and we're in fifth. The games come thick and fast and, with us not playing at certain times with the way they've fallen, we've just got to concentrate on what we do.
"That's all we can affect and, with six games to go, we hope to pick as many points up as possible to get us back in the top four."
Spurs host Manchester City on Sunday before travelling to Wigan Athletic the following Saturday.