Hal Robson-Kanu put the visitors ahead just after half-time but Darren Bent equalised soon after and it needed an 82nd-minute strike from Yakubu to settle the match in Reading's favour. Derby had Stephen Warnock sent off for a second yellow card in the 39th minute.
McClaren said: "The way we continued to set about a good Reading side in such a positive way made me very proud.
"You can hardly expect to win a game when you are down to 10 for 50 minutes. It's well-nigh impossible but, my word, we had a terrific crack at it.
"We didn't want a replay. We didn't want any more on our plate. We wanted to win at the first attempt and we couldn't have shown more willingness to have a real go at it.
"Even a man down we looked the better side but we were eventually caught on the break and a well-taken goal from the Yak saw Reading through. As soon as I saw him warming up to go on I thought 'Oh no, not him!'
"I don't know how old he is now - I didn't really know his age when I signed him for Boro and he was telling me he was only 25 - but he'll always have that pace and ability to finish."
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