Colombia will face Brazil in the next round on July 4, and Rodriguez warns that his teammates have acquired a taste for victory now.
"We're very happy because we are making history," Rodriguez, who leads the race for the tournament's Golden Boot with five goals, told FIFA.com.
"As a younger man, I always wanted to be here. That was a great dream of mine and we hope that we can make it far.
"It is a dream and we are making history and we want to do even more because this is a team that wants to win a lot."
Friday's clash with the host nation kicks off at 9pm.