Tottenham picked up just two points from their opening three games of last season, and ended up two points behind fourth-placed Arsenal in the table.
Spurs face newly-promoted Crystal Palace in their curtain-raiser on Sunday, and Dawson wants three points.
"We didn't get off to a flyer last season like we wanted to," he told the club's website.
"We showed strength, commitment and spirit to fight back, but if we had started better then who knows where it would have taken us? Hopefully this year we can get off to a flyer.
"Hopefully it will be the start of a great year that has more ups than downs."
Roberto Soldado, Paulinho, Nacer Chadli and Etienne Capoue have all joined the club, though their arrival has been overshadowed by the saga of Gareth Bale's possible move to Real Madrid.
Dawson has been impressed by the four new additions, especially Soldado, who has scored 20 goals per season for Valencia over the last three campaigns.
"He can send you here, there and everywhere with his touches and movement. I know, I've seen it in training," he said.
"He is a top signing and he is someone that I am sure the fans will come to adore. Nacer and Paulinho have signed too.
"It's important to bring new players in to freshen things up. I don't think you can ever stand still. Everyone is hungry to do well. It will improve us as a squad."