Spurs' run in Europe was one of the highlights of last season as they went about dismantling Italian giants Inter and AC Milan en route to being knocked out by Real Madrid in the quarter-finals.
But erratic form in the league saw them drop out of the running and finish fifth and so play in the Europa League this term.
Captain's job: Dawson is backing his team to return to thr Champions League
But captain Dawson says his team-mates are confident of booking a spot once again in the Europe's elite 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.'
And Dawson has pointed to the strong team ethic running through the side as proof they have what it takes to maintain their challenge.
Euro dream: Spurs set the competition alight last season
'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.' CLICK HERE TO SIGN UP FOR OUR FREE FANTASY FOOTBALL GAMESpurs' striker search could be over as Redknapp targets Twente forward RuizTottenham fear riots could threaten opening Premier League match against EvertonAll the latest Tottenham news, features and opinion