A penalty shoot-out win over city rivals Atletico Madrid saw Madrid win their 11th European crown after a tense 1-1 draw at San Siro on Saturday.
Zidane, who lifted the trophy as a player in 2002, becomes the second man to have gone on to win it as coach at the Santiago Bernabeu, following in the footsteps of former midfield great Miguel Munoz.
And Pepe could only praise the impact the former France star has had at the club since he replaced Rafael Benitez in January.
"We worked well with Benitez, although things didn't go well with him, and Zidane gave us a different air," he said. "He trusts us a lot, he understands the dressing room. He has given us the composure to finish the season really well.
"I'm happy because it's been a tough year for us, especially the first six months. Although everyone criticised us, we were always down to earth and quiet, working with great humility.
"I'm happy to help my team and give joy to Real Madrid fans who are celebrating the Undecima after a really tough match, at a really tough level mentally."
Pepe conceded Madrid were fatigued for much of the latter part of the match, in which Yannick Ferreira Carrasco equalised following Sergio Ramos' first-half opener, but he praised the battling qualities of his team-mates.
"We started very strongly and Atletico had no shots on goal throughout the first half, but then we tired and that hindered our work a lot," he said.