The 40-year-old Welshman had little luck on Wearside on Tuesday night as his side slipped to a 2-1 first-leg defeat, leaving them with a lot of work to do when the sides meet again on January 22 to determine who will make the trip to Wembley.
Giggs rattled the bar with a deflected shot, denied Adnan Januzaj a third goal at the Stadium of Light this season with an unwitting block from an offside position and then bundled Wes Brown's cross into his own net, and all that before the break.
"We did not have that little bit of luck," Giggs admitted. "I hit the crossbar and Adnan hit a shot against me when I was offside.
"On another day that would have gone in or been given, but it just did not go for us. We are still in it and we look forward to it at Old Trafford."
Giggs was aggrieved at a couple of decisions that went against United, the first a free-kick which led to Sunderland's opener, the second a penalty decision after Tom Cleverly tripped Adam Johnson.
"I thought both decisions were harsh," Giggs said. "I thought the first one was a free-kick to us - but saying that, we still have got to defend the free-kick.
"We got punished for that. We created enough chances, but unfortunately the decisions went against us. We were quite happy with our performance. The only chances they really had were set-pieces. It was just one of those nights."