A win at home to Sunderland on Sunday would see Tottenham surpass the club's record points haul in the Premier League era - but it will not guarantee a top four place.
But, while he is content with his side's efforts, Dawson acknowledges it would not be a "fantastic" season should Arsenal beat Newcastle and condemn Spurs to fifth place.
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|11/1||Tottenham are 11/1 with BetVictor to beat Sunderland 3-1 on Sunday
"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."
Dawson, who also narrowly missed out on a Champions League spot with Spurs seven years ago after much of the squad developed food poisoning, insists his side will do all they can on Sunday.
But he recognises they need Newcastle to prevent Arsenal from winning in order to finish in the top four.
"All we can do is concentrate on what we do, and fingers crossed Newcastle can do us a favour," he added.
"We have just got to go out there and get three points and see where it takes us on Sunday evening.
"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."