Rojo scrambled in the winning goal for Argentina as they edged Nigeria 3-2 in Porto Alegre on Wednesday, with Lionel Messi scoring a fine brace.
Alejandro Sabella's men sealed top place in Group F and set up a round of 16 clash against Switzerland on Tuesday.
Rojo, 24, is predictably excited by the knockout stages.
"Now a whole new competition begins," he told FIFA.com.
"There's no longer any margin for error. We either win or go home. As far as I'm concerned, it’s the best part of the tournament."
Rojo's scrambled effort from a corner was his first international goal and the Sporting Lisbon defender was delighted it came at such a good time.
"To score my first goal for Argentina, and for it to come at the World Cup and to secure three points for us – that's what dreams are made of," he said.
"I couldn't ask for more, although it wasn't a particularly beautiful goal."
As for Messi, who has scored an equal tournament-high four goals, Rojo is just happy to watch the Barcelona superstar from defence.
"Being able to watch him from the back is such a fantastic experience," he said.
