"The club considers that the refereeing did not adhere to the current law, directly influencing how the game progressed and the result," the club said in a statement.
The incident occurred after 54 minutes in Wednesday's game in Barcelona with Atletico leading 1-0.
Atletico defender Marc Pubill touched a ball passed to him by goalkeeper Juan Musso with his hand, to set it still in order to take the goal-kick himself.
Romanian referee Istvan Kovacs did not award a penalty, sparking outrage among the Barcelona players and staff.
Five-time Champions League winners Barcelona, who last lifted the trophy in 2015, said the "decision, along with a grave lack of intervention by VAR, represents a major error".
The club claimed that "this is not the first time in recent editions of the UEFA Champions League that unfathomable refereeing decisions have had a detrimental effect on the team, creating a clear double standard and preventing competing against other clubs on a level playing field".
The second leg is next Wednesday in Madrid.