Both of Aguero's boots caught the upper part of Luiz's left leg in the second-half of City's 2-1 win at Wembley, but the FA decided to take no action against the Argentinian.
Luiz avoided serious injury, but called for an apology from Aguero after the match and the City star has expressed his regret about the tackle.
"I've contacted @DavidLuiz--4 and apologized for what happened during the match," Aguero wrote on his official Twitter account, @aguerosergiokun.
"It was an impulse reaction that shouldn't have happened."
And Luiz later responded: "Thank you @aguerosergiokun for a demonstration of character. We get to know great man and athletes this way."
The Football Association confirmed referee Chris Foy had seen at least part of the incident and acted on it during the match, meaning the governing body were unable to deal with it retrospectively.