Big things were expected of Falcao when he joined United in a season-long loan move from Monaco almost five months ago.
Falcao had spent a long spell on the sidelines due to a knee injury before sealing his switch to the Premier League and has made only 14 appearances for United, scoring just three goals.
United manager Louis van Gaal has challenged the 28-year-old former Atletico Madrid man to prove himself, and Pekerman is confident Falcao will come good.
He told Caracol Radio station, as reported by Copa America's official website: "It's a difficult period for him, but he's a proven player with regard to his mentality and he'll keep on working hard.
"I'm sure that this [difficult period] will just be temporary and he will come through it, I don't have any doubt.
"The most important thing is that he is well [after his injuries].
"Sometimes these situations are not easy... it's a shame because he's a lad we want to be playing regularly as he's a great player, but I expect it will sort itself out soon."
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