Coach Jose Pekerman said Colombia have "placed everything" at the feet of James Rodriguez, who delivered with two goals in their victory over Uruguay on Saturday.
The 22-year-old Rodriguez provided the only scoring of the match, leading Pekerman to say "good players made the difference" in the round of 16 clash.
"As he's been doing in each match, he's been essential," Pekerman said of Rodriguez. "He's given us a lot and takes over. One always expects that such a young player plays well technically, and he does that, but has also grown a lot in having that responsibility.
"In my experience, I've had extraordinary football player, elite players. I've placed everything in James and what is most surprising at this young age; he has no problem with being responsible for doing things that take football players a long time to achieve.
"Football forces you to deal with a lot of situations. You have to handle these situations. He has everything of a top-notch player. I praised what he's doing and never had any doubts that this would be James Rodriguez's World Cup."
Rodriguez, who scored nine goals for Monaco last season, said Colombia "is a team that wants to win a lot."
"I only want to help so that the team can win," he said. "I want to do my share so that Colombia can make it far. I'm at a good level and we are scoring goals. I'm very happy for that."
"You must always have a plan of how you are going to play. You follow your own plan. In each match, we've always done that and against Brazil, this is not going to change."
Colombia reached the World Cup quarterfinals for the first time in their history, but an even bigger challenge awaits in hosts Brazil.
"We can expect a match with a lot of tension, but because of the attitude of the teams, it could be a match with goals and good play," Pekerman said. "That will be good to the World Cup at this stage, even with pressure.
"We will always respect Brazil. They are a great team and we know that everyone in the World Cup goes through difficult moments at some point, but they have been overcome. We cannot speak of favourites, but we must understand it is a new match. Colombia are playing well as a team and in an intelligent manner. We know that the match will be hard and Brazil has enough talent to cause us some concern.
"We never lost our hope. We always had the idea that we were going to be a part of a competitive group. We knew that the group would be complicated for a team that had not been in a World Cup for a long time. We're now achieving the results, and now, let's seen how far they will allow us to go."