The last time Spurs finished above the Gunners was in 1995 - before manager Arsene Wenger took charge.
"We have to,” explained Villas-Boas.
"By what I see, it's obvious that Man United, Man City and Chelsea are into a big running towards the title."
He added: "To play for that fourth spot, I think you know it's difficult bearing in mind the amount of competition you have to beat."
"Recently, they have obtained more Champions League qualifications, so our objectives for the season have been within their reach for the last couple of years.
"We are certainly getting nearer in terms of what we are doing for the club, but the past shows that at the moment they are regular in obtaining those sorts of objectives."