Aguero, making his first appearance since June after a knee injury, disputed a throw-in call which went against him early in the second half of the match before touching Massey-Ellis as she turned to walk away.
His actions drew criticism on social media and led his former team-mate Micah Richards to say on Sky Sports that Aguero should “know better”.
Under rules introduced in 2016 players can be cautioned or sent off for touching match officials depending on the nature of the incident, but Aguero’s actions went unpunished at the time.
After reviewing the incident, the Football Association is satisfied that match officials did not believe any formal action was necessary.
City manager Pep Guardiola defended Aguero in his post-match press conference, saying: “Come on guys. Sergio is the nicest person I ever met in my life. Look for problems in other situations, not in this one.”
Aguero, who played a key role in setting up Raheem Sterling’s decisive 23rd-minute goal, was replaced after 65 minutes of his comeback appearance.