The Eredivisie title holders were allocated a place in Group D alongside the champions of La Liga, the Premier League and the Bundesliga in Europe’s most prestigious club competition.
Speaking to reporters after the draw in Monaco, De Boer maintained that his players must harbour no fears when they meet their opponents in Europe, insisting they will adhere to their principles.
“The pressure is on the other teams,” the 41-year-old said. “We're just going to play our own game.”
De Boer believes being drawn with Real Madrid for a third consecutive season gives the Dutch powerhouse a chance to show how strong they are, as he analysed the other teams in the group.
"Against Real, we can prove our worth again. Last season we had a good match in Madrid and two disallowed goals at the Amsterdam Arena.
"City have an incredible quality in defence, which is very solid. And they have five or six lethal strikers to choose from, meaning they can score at any time. They're just a strong team.
"And the same goes for Dortmund, who won the title in Germany twice in a row. Bayern Munich went to the final of the Champions League, but Dortmund won the championship twice. That says something about the power of BVB."
Ajax start their Champions League campaign in Germany on September 18 when they face Dortmund.