Star Monaco striker Falcao is in doubt for Brazil 2014, struggling to recover from a knee injury suffered in January.
Falcao's absence would be considered a huge blow to a nation who are considered a dark horse for the tournament.
But Toulouse midfielder Aguilar said that was not the case.
"Falcao is an icon, an excellent player and very important for the team, but our work and our progress owe everything to our collective efforts, which have served us well so far," he told FIFA.com.
"We all hope he'll be there but it would be a mistake to think that we'll be weaker without him. We need to convince ourselves, and our opponents, that everything we're capable of we do as a team."
The fiery Aguilar has had two heated run-ins with Barcelona and Argentina star Lionel Messi, as well as another with Paris Saint-Germain striker Zlatan Ibrahimovic.
But the 29-year-old said that was simply his style, while insisting they were confrontations that remained on the pitch.
"I only care about the game, not the name, career or the medals of my opponent," Aguilar said.
"I always play with the same desire, whether I'm up against Messi, Ibrahimovic or someone else. I have to show that I'm here and that I'll give everything to win every ball and help my team.
"That's my style of play and if I've had clashes with those players, it's because it was the thing to do during the game.
"Those are situations that happen during a match but they stay on the pitch and afterwards I don't feel any bitterness. It's already forgotten."
Colombia face Greece, Ivory Coast and Japan in Group C at the FIFA World Cup.
