The Manchester United loanee broke the deadlock for the South Americans with a powerful header early on in the game.
Falcao told reporters: "Colombia will have to give 100% to beat El Salvador and Canada [on Tuesday], and on the other hand, we take the opportunity to continue to grow as a group and improve.
"The most important goal is the World Cup in Russia in 2018, but there are also short-term goals and we want be the best we can be. Colombia is ready for big things."
Falcao is on a season-long loan at Old Trafford from Monaco.