Last season, Spurs finished above Arsenal in the league for the first time since 1994/95, sparking talks of a power shift in north London.
However, Pochettino has urged fans to look at the bigger picture and says it is far more important to start winning major trophies.
In an exclusive interview with 'Sky Sports', the Tottenham boss said: "Of course, it was a massive achievement last season to be above them after 22 years.
"But our objective is a great project to try to give Tottenham the possibility to win titles, the Premier League and the Champions League.
"I think that is our challenge, it's not to be above Arsenal.
"We understand that Tottenham fans want to beat Arsenal and to be above them, but I think our project is not only to be above Arsenal, it's to be above everyone and to be at the top and win titles.
"That is our challenge."
Spurs have won just one of their last 24 league visits to Arsenal, but Pochettino insists his players are in a confident mood ahead of what is sure to be a fiery encounter.
"Of course we believe we can win," he added.
"In football you can be up or down very quickly and the challenge is now to keep at the level that we've got in the last few years."