Falcao started in United's 2-0 win over QPR on Saturday after he was axed from the 18-man squad against Southampton six days earlier.
Speculation has mounted over whether United will sign the Colombian hit man on a permanent £43m deal in the summer, following his worrying injury record.
"I am fine. I feel really good," Falcao said.
"I am playing without any sort of fitness problems. It was 90 very important minutes for me. I need to play and I am very happy I did."
Falcao, who missed a couple of presentable opportunities against the Hoops, is hoping his luck in front of goal will change soon.
GETTY
Radamel Falcao in action for Manchester United against QPR
I feel really good. It was 90 very important minutes for me. I need to play and I am very happy I did
Radamel Falcao
"Obviously, I really hope to score soon but the opportunities will come, I am sure of that," Falcao added.
"I am very happy with the win. It was a difficult game but we managed the match well and got the three points.
"I could have had two goals. Sadly, the goalkeeper did very well and the other chances were not that clear."
Falcao has managed just three goals for United since joining them on a season-long loan deal from Monaco last summer.
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