Spurs overcame the likes of AC and Inter Milan on what was their debut campaign in the tournament last season to reach the quarter-finals, where they were ultimately ousted by Real Madrid.
However, the North Londoners failed to book a spot in the continental competition for the second successive year, missing out on a top-four Premier League finish to Arsenal.
Manager Harry Redknapp has admitted that Spurs might not be able to keep up with their big-spending rivals this season, with Manchester United, Manchester City, Chelsea, Arsenal and Liverpool expected to be battling it out to finish in the top four.
But captain Dawson refuses to give up on the prospect of clawing back a spot in club football's top competition.
"We're aiming to be in the top four, we've been in it, and the lads are hungry to be in it again," Dawson told The Independent.
"Of course you're disappointed not to be in the Champions League. It's where you want to be playing, and you speak to the fans - we travelled with thousands everywhere we went and they loved it as much as the players.
"You want to be playing against the best players but you've got to earn the right to be back there."
Dawson believes Spurs have already proved that they can hold their own against their top-four rivals.
"We were 2-0 down to Arsenal (last season) and came back to win 3-2," he said. "We had a little dip towards the end of the season, but we showed character by winning at Liverpool 2-0, where we haven't won for a long time, and finishing fifth.
"We're going to these places where maybe five or six years ago we weren't getting wins, so we're moving forward.
"We know it's going to be tough, but we've got top players and we'll be giving it our all this year."