They managed to hold on and book a semi-final against Germany, with Luiz admitting that the South Americans will have to be at their best to beat Joachim Low's side.
"I want to congratulate both teams for this great game - Colombia made a great World Cup and fought until the end," he told reporters. "Our team played beautiful football that everyone likes, with a lot of intensity, seeking the goal every moment.
"It will be another great game against Germany, a world derby. I hope that we can be at our best level as they have a great team.
"They always play the same way with a lot of consistency. It will be another beautiful game."
Brazil and Germany's semi-final tie will take place next Tuesday at the Estadio Mineirao in Belo Horizonte.