Head coach Marc Wilmots' men are seen as one of the outsiders to win the competition after wins over Algeria, Russia, South Korea and USA and Vertonghen is confident they can spring a surprise against the South Americans.
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"We have all been looking forward to this tournament. It's all about games like this for us. But it doesn't have to stop here against Argentina.
"We want to put in a great fight and go even further. This is all a reward for our hard work."
Vertonghen went on hail Lionel Messi's form for Argentina at the World Cup but insisted that Belgium cannot afford to focus solely on the Barcelona man.
"Messi has been outstanding so far. He's obviously Argentina's main man. There are more players to watch, but he has been outstanding.
"I spoke with Dries Mertens about Gonzalo Higuain. He is a big fan of him and has warned us that he's a great player.
"And they have Ezequiel Lavezzi and Angel Di Maria as well. We will have to be on top of our game."
Wilmots, meanwhile, believes that the match against Argentina will be decided by small details, but is confident Belgium will be up for the challenge.
"We are ready for Argentina. Everything is possible. Details will be decisive. The game could be decided by an individual action, by a minor mistake. I hope we make fewer mistakes than them.
"We don't feel any pressure. We are hungry for success. We have our own philosophy. We have a winning mentality.
"If we go out but put in a great performance and show what we're worth, we will still go home with a feeling of satisfaction."
The Belgium boss then went on to defend Eden Hazard in the wake of his relatively disappointing performances so far and stressed that the Chelsea man has been playing his part for the team.
"I don't think Eden has been lacking anything this World Cup compared to how he does at Chelsea. He's part of a team and works together with Jan Vertonghen down the left," he added.
"He's eager to learn and to make progress, but all as part of the team. It's not about individuals. We don't want to depend on one player."