United scraped into the Europa League semifinals via a questionable penalty converted by Bruno Fernandes.
Together with goalkeeper Karl-Johan Johnsson, Falk was outstanding on the night.
Solskjaer told bold.dk: "He delivered a fantastic performance. He gave us problems both when he played left and right. Technically, he is really, really good. He is fast and he turns on opponents for fun.
"We also saw this in the match against Istanbul, where he tipped the ball around a defender inside the field and almost scored.
"He created FCK's biggest chance with a fantastic move, where he played it back to Jonas Wind, but it luckily ended with a good block from Aaron Wan-Bissaka..."