Manager Sir Alex Ferguson reacted angrily after Nani was sent off for a high challenge on Madrid's Alvaro Arbeloa in the 56th minute of the match, which United were leading 1-0 at the time.
But with the man advantage, Madrid came back to win 2-1 on the night, 3-2 on aggregate.
Ferguson did not appear for interviews after the match, with his assistant Mike Phelan attending the post-match press conference and saying the manager was too "distraught" to speak, while the players did not stop to talk in the mixed zone.
UEFA earlier said it had "no problem" with referee Cuneyt Cakir and backed his decision to dismiss Nani.
"We have no problem with him," a UEFA spokesman told the Guardian.
"There are no issues for us regarding the sending off and we will wait for the official reports of the match delegate and the referee's observer, as is procedure. If they raise concerns then we will act."