The Swiss sprang a surprise 1-0 win over favourites and reigning European champions Spain this week and the Swiss left-back felt their pragmatic approach was key.
"I think our strength is the organisation of the team. They had a lot of ball possession but we knew that [would happen] before the game," he said. "I think the difference was in the organisation of Switzerland. We played well and we were more aggressive in one against ones. They wanted to play well against us but it was hard for them."
The Sampdoria defender said that victory had given them confidence for the game against Chile, who also have three points in Group H, on Monday.
"Beating Spain is a good feeling," Ziegler added. "The first game in the tournament is always hard so we are all proud to have won this game against one of the best teams in the world.
"Now we have to concentrate on playing well against Chile because it's not good to win against Spain and then play a bad game the second time. We know we did something big and we all proud for the country but now we have to concentrate against Chile because it will be another hard game."