Spurs looked set to secure a spot in the competition for 2013/14 but they missed out on a top-four Premier League finish after being overtaken by north London rivals Arsenal and centre-back Dawson is keen to make amends.
"We missed out on the Champions League last season so our aim at the start of this campaign is to make sure we are in it next year," said Dawson.
"We have to fight for that."
Some commentators have suggested Andre Villas-Boas' side will benefit from both Manchester clubs and Chelsea finding their feet after installing new managers ahead of the new season.
But Dawson dismissed that theory and argued no one knows who will perform well at the start of a campaign.
"You could say there was uncertainty before any season," he added.
"You have to earn the right to win the Premier League. Manchester United did it last season and they will no doubt want to do it again.
"They are a top class team and have been for years. Manchester City have strengthened again, so they will be fighting.
"Chelsea, with Mourinho back, are clearly aiming high. Arsenal, ourselves, Liverpool.
"Everyone wants to be in the top four and back in the Champions League."