Spurs failed to qualify for the competition seven years ago due to a dodgy lasagne and missed out last season after Chelsea's victory in Munich.
If Spurs beat Sunderland they will end with 72 points - a club record in the Premier League era, but that will be of little consolation if Arsenal beat Newcastle and they miss out on fourth.
The Spurs skipper said: "If we win and get 72 it will be a great season, but it will only be a fantastic season if we get that Champions League spot.
"That's what we set out to achieve at the start of the season.
"If we can get that number of points then great, but we want to be in the Champions League with the way we missed out on it last year."
Tottenham's 2-1 win over Arsenal on March 3 left the team seven points clear of their rivals but, just like last year, their form has dipped in the last quarter of the season, winning just four out of their Premier League fixtures since that date.
Newcastle have won just three of their last 10 games but Dawson believes there may be one last twist in the tale.
"All we can do is concentrate on what we do, and fingers crossed Newcastle can do us a favour," he said.
"We have just got to go out there and get three points and see where it takes us on Sunday evening."
Arsenal's 4-1 win over Wigan on Tuesday means Sunderland are safe, but manager Paolo Di Canio has made it clear to his players that he will not tolerate any sub-standard performances tomorrow at White Hart Lane.
The Italian this week called on his players to end the season "with dignity" and threatened to cut short the number of holidays taken by squad members who are not pulling their weight.
Dawson is sure the Black Cats will be giving it their all as a result.
"I don't think it will make a difference (that they are safe) with Paolo Di Canio," the centre-back said.
"He will have them riled up. He will want to get 110 per cent commitment from them.
"They will want to put on a performance and we have to make sure that we stop that and play the way we know we can.
"The atmosphere will be great. It's the last game of the season and hopefully we will get the three points and it will be good enough."