Falcao thrilled to have scored in front of the Old Trafford faithful[EPA]
The 28-year-old striker, who joined United on a season-long loan, latched on to a wayward Angel Di Maria shot to claim his first goal in what proved to be the winner.
The strike lifts the Red Devils into the top four of the Premier League, and the Colombian hopes it's the first of many.
"All strikers need goals, and for me there was a little bit of relief to score my first goal," he said. "I hope to score many in the future.
Van Gaal hails De Gea [AMBIENT]
There was a little bit of relief to score my first goal
Radamel Falcao
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"It was amazing that my first goal was at Old Trafford, I enjoyed it with all the fans and I want to say thank you to God, my team mates, all the staff and the coaches."
Boss Louis van Gaal had spoken to the 28-year-old about being more relaxed, saying: "He needed that goal.
"I talked with him and I told him that he was forcing himself too much to score. Now he has his, it will be better after the international break."