The European champions booked their place in the last eight thanks to a narrow win over the Portuguese with star striker David Villa netting the only goal of the game at the Green Point Stadium in Cape Town.
"With this team we can dominate any game and we have done what we needed to do," said Pique. "We knew it would be very hard.
"After the goal we completely controlled the game and they created little danger. In the second half we have shown the business of a championship team.
"The victory was necessary and now we think of Paraguay."
Ramos was impressed with the level of performance his team displayed against the Portuguese, but insisted that they must respect Paraguay if they are to progress to the semi-finals.
"The important thing is the team," said the Real Madrid right-back. "We are at a high level, but this is the World Cup.
"We faced a tough opponent and had to be careful because they have fast players capable of catching you on the counterattack. After the break, we regained the confidence and kept our pace.
"The group is good but we should not disrespect any team."