The 27-year-old attacker has taken a central role in Madrid's squad since his £80 million (€94m) transfer from Manchester United in 2009, scoring 128 goals in as many appearances for Los Blancos.
Portugal's fans expect the same level of form in Poland and Ukraine this summer, where the Seleccao must face Germany, Denmark and the Netherlands in the group stage, but Pepe warned that too much pressure on Ronaldo may affect his game.
"I think Cristiano has always had a lot of responsibility since he was 18, and people put a lot of pressure on him," Pepe told Uefa.com.
"People now understand the importance of the squad. The squad needs to give support to Cristiano, so that he can be calm and play his football."
Pepe opened the scoring for Portugal at Euro 2008 with a goal against Turkey, but the 29-year-old defender has guaranteed that he is more focused on defensive tasks now.
"I was younger," Pepe noted. "I did not really know about the responsibilities of playing at a Euro, and finishing off moves like that.
"Obviously, I like to take the odd risk like that to help my team-mates out up front, but first and foremost a central defender needs to defend, and defend well.
"[But] if I get the chance to make a play like that one against Turkey, obviously I will look to take it."