Turkish referee Cuneyt Cakir dismissed Nani after his boot connected with Alvaro Arbeloa's chest as they went for a high ball.
United had been winning 1-0, but Real ended up 2-1 victors to progress to the quarter-finals 3-2 on aggregate.
Keane though insisted on ITV the red card was justified.
He said: "I think the referee has actually made the right call. Everyone's upset about it and it's slightly unlucky, but it's dangerous play. Whether he meant it or not is irrelevant.
"It's dangerous play - it's a red card.
"You have to be aware of other players on the pitch. Does he think he's going to have 20 yards to himself?
"Whether it's [a brave decision] or not, it's the right decision. Whether he meant it or not doesn't matter.
"Nani's a quick boy to go down anyway. He's not the bravest player on the planet."
Keane insisted the referee had carefully considered his decision.
He added: "It doesn't matter if he knows there's somebody there or not, it's irrelevant. I don't think the referee actually made the decision because he waited a couple of minutes while the player was getting treatment.
"I think it might have been the assistant that made the decision, and I actually think he's made the right call.
"We always say referees are very quick to make decisions - he waited a couple of minutes.
"Any time I was sent off in my career I always thought, 'did I give the referee chance to send me off?' And if the answer is yes, then it's out of your hands."
Former United full-back Gary Neville had a different view to Keane.
He wrote on Twitter on Wednesday morning: "Been going to OT since age of 5 and I've never seen the whole ground as in disbelief as they were last night at a decision!
"Nani is a player who regularly tries to control a pass like this over his shoulder and its never a red card! Changed the whole game!Poor ref.
"The crowd actually weren't angry / weren't shouting they were just open mouthed and in shock!"
Neville felt that if Nani deserved red then so did Madrid goalkeeper Diego Lopez for making contact with Nemanja Vidic when the United defender got his head to a corner ahead of the keeper.
"The Madrid keeper on Vidic looked a similar type of incident," Neville added.
"Anyway it won't be the first time or last! Just ruined a fascinating match and didn't feel right to Utd or Madrid people in the stadium!"
Chopper - "Why cant fergie do better in Europe?" - Because every year there are at least 5 or 6 teams capable of winning and no team is entitled to success in this competition. He's made the semi-finals 5 or 6 times, and made 4 finals in all, winning two of them and losing the other two to the finest club side Europe has seen for more than 30 years.- HarryBoulton