The United defender was unhappy with the decision of Cakir to send off Nani after 56 minutes when Sir Alex Ferguson's side were in the lead.
Real went on to secure a 2-1 victory in the last-16 second leg clash at Old Trafford to advance 3-2 on aggregate and Ferdinand expressed his displeasure at the final whistle.
But after evaluating the referee's report of the game, UEFA have decided not to take the matter any further.
"From the report we have received from the referee we will not take any action apart from the disciplinary proceedings against Manchester United for the red card of Nani and for post-match media obligations not being fulfilled," said a UEFA spokesman.
Wayne Rooney was not so fortunate after he was sent off in 2005 after being shown a second yellow card for sarcastically applauding referee Kim Milton Nielsen during a 1-1 draw against Villarreal in the Champions League.
UEFA's disciplinary body will also decide if Nani's dismissal for a high challenge on Alvaro Arbeloa is worth more than an automatic one-match ban.
United manager Sir Alex Ferguson could be in trouble for refusing to speak to any media after the game, which breaches UEFA's Champions League regulations.
No United player was made available to the media either, which also contravenes competition rules.