The Australian goalkeeper made a string of fine saves in the 2-1 defeat at Old Trafford as the Royals were knocked out in the fifth round of the famous cup competition.
In particular, Federici was brilliant early in the contest when United were full of attack but he managed to keep Sir Alex Ferguson's stars at bay for the most part before Nani and Javier Hernandez gave the home side a two-goal advantage.
"Their manager, Sir Alex Ferguson, he knows how to get results and I think he'll be quite relieved tonight knowing that his side have gone through," said McDermott.
"Feds was tremendous. He made some really, really good saves, especially when we were under the kosh a bit in the first ten or fifteen minutes.
"But at the other end Alfie (Adam Le Fondre) hit that chance and he hit the target, but their goalkeeper (David de Gea) has made a fantastic save of his own. And then they go up the other end and score their second.
"It could have been 1-1 and seconds later it's 2-0. But I'm pleased with everyone of them out there - it was a real good effort."