The Colombia hitman missed the World Cup after suffering knee ligament damage with AS Monaco in January, before making his comeback against Brazil recently.
It was the 28-year-old's first appearance on a football field since sealing a deadline day move to United.
Falcao has enjoyed goal-laden spells with Porto and Atletico Madrid, and the striker feels ready to replicate those feats during his season-long loan spell with Louis van Gaal's side this term.
"Because of the injury I felt so nervous," he told reporters. "Almost like it was my first time with the national team [against Brazil].
"And I expect it will be the same before I play my first game for Manchester United. I'm so happy to be back, and I am also happy about being able to join United.
"Physically I feel spectacular. I have been able to play without any kind of trouble. I am very excited about playing for Manchester United, and I hope to score a lot of goals for them. That is something I have done everywhere I have played."
Falcao could make his debut against Queens Park Rangers next Sunday, if his visa application is processed in time.