The powerful defender believes the Liga giants surprised everyone with their strong performance in Gelsenkirchen against Schalke
Goals from Karim Benzema and Gareth Bale helped Madrid to a two-goal lead at half-time before Cristiano Ronaldo made it three shortly after the break.
Bale, Benzema and Ronaldo doubled their personal tally in the remainder of the game, with Klaas-Jan Huntelaar's injury-time strike nothing more than a consolation goal for Schalke.
"To be honest, I didn't think a game like that was possible at this stage of the competition, but we put in a strong performance from the very start and all the goals were well worked," Pepe was quoted as saying on the official Uefa website.
The centre-back then went on to praise Madrid's attacking trio, but insisted that the entire team put in a strong display.
"The lads up front did really well, but it wasn't just them – it was a great performance from the whole team," he continued.
"We're all physically fit, mentally strong and have the composure to win games like these. That's what makes the difference at this level."
Madrid resume La Liga action on Sunday when they take on city rivals Atletico.