The Colombian revealed on Twitter the UEFA president's prank when receiving his medal at the Europa League final on Wednesday
The Colombian proved lethal at the National Arena in Bucharest, scoring two first-half goals to set Los Colchoneros on their way to a 3-0 victory over Athletic Bilbao and secure their second Europa League title in three years.
The 26 year old secured his second European title in as many years, after firing Porto to glory last season in Dublin - a fact not missed by the Frenchman.
"We were in line waiting for the medals and the delivery of the #UEL [Uefa Europa League]." Falcao revealed to his followers on Twitter.
"I approached the great Michel Platini who put the medal on me and removed it again. I looked at him and he says 'you again?!', before finally giving me my medal."
"He shook my hand with a smile, handed over the trophy, and the celebrations exploded!"
Falcao and Atletico Madrid return to domestic action on Sunday evening away to Villarreal, with Diego Simeone's men aiming to beat Malaga to fourth place and the final Champions League qualification berth.