Alejandro Sabella's men downed Netherlands 4-2 in a penalty shoot-out to advance from their semi-final on Wednesday, and into the decider against Germany on Sunday at the Estadio do Maracana.
Aguero, a second-half substitute in Sao Paulo, said their triumph went against the expectations on his side pre-tournament in Brazil.
"A lot of people didn't think Argentina would get to the final but we knew what players we had, very good players individually," said Aguero, who put his side up 3-1 in the shoot-out.
"This means so much."
Maxi Rodriguez, who tucked away the decisive penalty after normal and extra time finished 0-0, said Argentina's first World Cup final appearance in 24 years was deserved.
"We know the pain we have been through, and we deserved some kind of happiness," said Rodriguez, who only came on in the second half of extra time.
The Newell's Old Boys midfielder said the result was emotional for players and fans alike.
"Now we have to play the final but that is what we have dreamed of ever since we left Buenos Aires," Rodriguez said.
"We must make the most of it and let's hope that the last 90 minutes are on our side.
"I dedicate this to my family and all of Argentina, to everyone who is crying like us, who have had a dream since they were little and now might be able to see it fulfilled."
