Spurs have made a solid start to their Premier League campaign and collected 20 points from their first 11 games, but last weekend's 1-0 loss at home to Newcastle United left them seventh in the table.
Dawson remains upbeat about Tottenham's chances of qualifying for the UEFA Champions League and insists they are even capable of challenging for the title.
"Our expectations are high," he told the Daily Star Sunday. "There's no hiding at the start of the season. Our aim was to be in the top four. That hasn't changed.
"But we aim high and we believe that we have got the squad - and the quality in the dressing room - to go all the way."
Dawson has been part of a defence which has conceded just six league goals so far this season, and he believes that is a great foundation to build on.
The centre-back is convinced that Spurs' attacking players will soon start to click into gear, having scored just nine times to date, and drive the club on to a successful season.
He said: "It's great keeping clean sheets and I take great pride in that. As a team, we have worked very hard at that aspect.
"Yes, we would have liked to have scored a few more goals and turned a few more of the draws into wins.
"But we have had a great start. Our best in the Premier League. We have to take a lot of positives from that. And those goals will come.
"As the manager says, the aim is to win a trophy this season and we are going for every competition.
"But everyone wants to play every game and the squad we now have means that any team the manager chooses can do well in the Premier League."