He added: "This club is supported much better than the others, so that means it's a bigger club than the others.
"You've got to make sure that the fans are happy with you, and you do that by winning derby matches."
Asked whether those fans are right to expect to dominate their regional rivals, Allardyce said: "Absolutely, that's justified on the size of the club, the support that it gets and the money that's been spent over the years to try and get it to where it wants to go.
"It's got a big, big status, in terms of overall revenue and turnover, as well as in terms of its fans."
But the Newcastle boss admitted: "It's really good to have three teams in the area competing in the Premier League.
"In this country, the North East represents the third biggest area for Premier League football. You've got seven in London, seven in the North West and two in the Midlands - three if you count Derby.
"So there's big representation in the Premier League in this area.
"The ultimate achievement, obviously, is to win more matches than those two (Sunderland and Boro) and then make sure you get to where you want to go for the future, and that's a team that can sustain success."