The Ligue 1 leaders were 2-1 up in the last-16 first-leg clash when they were awarded a spot-kick early in the second half, but Falcao's tame effort was easily saved by Willy Caballero and Sergio Aguero equalised eight minutes later.
Despite Falcao then adding to his earlier goal with a glorious chip, further strikes from Aguero, John Stones and Leroy Sane at the Etihad Stadium left Monaco with plenty of work to do on home soil.
"We made a couple of errors in defence that we were punished for and I think the real key to this game was when we could have gone 3-1 up," the Portuguese lamented. "I think Monaco played a great game. I have congratulated my players.
"This game was perhaps one of the most exciting games of the Champions League this season, exciting for the supporters," he continued. "It was a great game for the supporter.
"I imagine everyone was happy to witness such a spectacle.
"We work hard to put on a show because we are passionate about football and we want to please the fans. Scoring three goals here at Manchester City is a really good show, a fantastic game.
"We've got 90 minutes to go, playing at home, so it’s far from over."