With United a man down, Modric came off the bench to fire Real level before Cristiano Ronaldo's winner settled the Champions League tie.
"The only thing I could think was, 'right, let's try and stay compact. Let's try and ride it out'," Giggs told the Mail on Sunday when discussing Nani's red.
"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."