The centre-back believes Portugal's desire to fight to the end was the key in their dramatic win over Group B rivals Denmark on Wednesday
The Real Madrid man gave Paulo Bento's side the lead when he headed in from a corner. Helder Postiga soon doubled their advantage, turning in Nani's cross, before Nicklas Bendtner pulled one back for the Danes shortly before half-time.
Bendtner looked to have earned a share of the spoils for Morten Olsen's team with a header 10 minutes from time, but substitute Silvestre Varela's late volley secured all three points for the Portuguese, a result which Pepe believes was no more than they deserved.
"I think we started the game well and we scored two very important goals," he told SIC.
"We almost killed off the match, but we missed two chances and we ended up allowing Denmark to equalise. But in the end Varela appeared and he gave us a great help with that goal.
"We knew about the importance of this game. It was crucial to get a victory and decide everything in this match. We tried to kill off the game on the counter, but we could not do it.
"After it was 2-2, we were very tired, but we were rewarded for our determination to fight until the end."
Portugal's fate will be decided on Sunday when they take on Netherlands in their final group game, and Pepe thinks that the win over Denmark will bring more focus ahead of the crunch clash.
"This result is very important. Netherlands are going through a difficult moment right now, with a bad atmosphere inside the team. We will see how they play against Germany. But we only depend on ourselves and we will step onto the pitch to win that game.
"We knew we could have defeated Germany, but we are much calmer with this victory. We will be calm and focused, with the same spirit showed today, in order to go through."