Arsenal beat Norwich City on Saturday to move up to third in the table, taking advantage of Spurs' lack of a match, while Chelsea occupy fourth spot with a game in hand.
It has been suggested that Andre Villas-Boas's team are suffering from fatigue after they exited the European competition to Basel but Dawson claims that their only regret is that they were not able to progress further.
|6/4||Tottenham are 6/4 with BetVictor to finish in the Premier League top four
"It's just that, after getting as far as we did, we wish we could have gone all the way. It would have been great to be lifting that trophy, but that's not going to be, so we'll be concentrating on the Premier League now."
The centre-back insists that Spurs are not contemplating the possibility of missing out on a place in the top four and qualification for the Champions League despite their recent blip.
"We're not thinking of [finishing outside the top four]," Dawson added. "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."