Spurs were outsiders to progress from their group having been drawn alongside champions Real Madrid and Borussia Dortmund, but won five of their six group games to finish with 16 points, the highest total in this season's competition.
The last two English teams to reach 16 points in the group stages were Arsenal and Manchester United, both of whom went on to make the final in 2006 and 2007 respectively.
Rose, who was subbed off 70 minutes against APOEL on Wednesday night, is hoping that Spurs can that run going but says that he knows how difficult it will be to progress to the latter stages of the competition.
"It's nice that we proved a lot of people wrong," Rose told talkSPORT.
"But now, whoever you draw, it's going to be a very difficult game and if you're going to get to the final, you're going to have to beat two top teams along the way.
"We've set the standard so there are no excuses now. We've beaten Real [Madrid] and Borussia Dortmund twice and we'll welcome any team we draw against in the next round."
The draw for the first round of the knockout stages takes place on December 11, with the North London side knowing that despite winning their group they could face European giants such as Bayern Munich or Juventus in the next round.