The Chelsea star admitted he has yet to hit form in the tournament as Belgium safely negotiated the group stages to set up Tuesday's last-16 game with the United States.
And with tournament top-scorer Rodriguez grabbing headlines with his fabulous double against Uruguay, Hazard said he was itching to play a decisive role for Belgium.
"I think that each match I've given my maximum. Since the start of the World Cup I haven't had a great match with good moves," Hazard said.
"I haven't had a good match that with good moves that could be decisive for our team. So I hope I can do that and have a good match."
He added: "I would really like it if I can get around the pitch more and see more of the ball -- and make a difference, basically."
He nearly opened his account after coming on in the final minutes of the 1-0 victory over South Korea, but saw an angled shot palmed away by goalkeeper Kim Seung-Gyu.
Belgium coach Marc Wilmots said he is still waiting for Hazard to "take hold of a match" and had discussed the problem with the 23-year-old.
Rodriguez scored three times in group play and he blasted Colombia into the last eight, first with a superb volley and then by finishing a team move to seal the 2-0 win.
"He played a super-good match. I knew who he was but most people didn't know much about Colombia," Hazard said of the 22-year-old Rodriguez.
"I think yes, his statistics are the best and he showed yesterday that he can carry a team. We thought it would be difficult for Colombia without (injured striker Radamel) Falcao. But he scored two superb goals."
Despite his indifferent start, the assured Hazard carried a look of intent as he spoke to reporters at Belgium's training base in Mogi das Cruzes, near Sao Paulo.
And Hazard said he would have no hesitation to step forward if the United States game goes to penalties.
"I hope it doesn't happen, because we'll all feel the pressure. But if we have to take them, I prefer to go last," he said.
Hazard added: "In qualifying it's easier because you have more matches. Now we've arrived at the stage where if you lose, you're out.
"It's multiplied by 10. One mistake and that could be it."
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- Eden Hazard
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