The AS Monaco striker had surgery on Saturday to fix to a torn anterior cruciate ligament in his left knee that he suffered in the Coupe de France last week.
"I am convinced that everything is going to be okay and I will be able to give the best I have [at the World Cup]," Falcao said at a press conference held at a Porto hospital. "When they told me at first that I had a serious injury and there was only a small chance of participating [in Brazil], I didn't care whether it was 10, 20 or 50%, I was counting on that chance.
"This is my hope and with this dream I will work every day. A lot has to do with my emotional state. This is something that I can manage each day. Without a doubt I think that time is not on our side but I think the possibility exists and that is where I find hope.
"I try not to think not to think about whether [recover] will be two, three, four months, but rather to focus on the day to day. I can't skip any steps. The main thing is that I can respect the recovery steps for a good rehab. At no time will I pressure myself of the capacity of my knee to recover."
Falcao is expected to check out of the Trinidade de Oporto hospital today.