The Portuguese's surprise dismissal turned out to be the turning point in the last-16 second-leg clash.
With the Red Devils leading thanks to Sergio Ramos' own goal early in the second half, they were suddenly up against it when Nani was given his marching orders for a mid-air challenge on Alvaro Arbeloa - to Giggs' incredulity in his 1,000th career match.
"I'd initially gone over to tell him Nani was looking at the ball," Giggs said in an interview with the Mail on Sunday. "I've gone back to my position on the edge of the box, because they've got a free-kick.
"I was actually looking at the referee when he did it (showed the red card). I've never, ever experienced a shock like it on a football pitch because I just didn't expect it. And I've never seen a stadium in shock like that."
Madrid boss Jose Mourinho brought on Luka Modric, who levelled proceedings with a fine individual effort in the 66th minute and United old boy Cristiano Ronaldo completed the comeback almost immediately afterward.
Giggs thought the hosts initially responded well to Nani's dismissal, but admits they were undone by Modric's excellence.
"The only thing I could think was, `right, let's try and stay compact. Let's try and ride it out'," added the 39-year-old.
"I think we did that. But you can't really say anything about the goal; it was brilliant by Luka Modric.
"There's not a lot you can do, going down to 10 men. Carra [Michael Carrick] was in the back four and he had to come out to Modric, close him down, whereas if we'd had 11, he would have been there probably. Take nothing away from Modric, it was a great goal."