Having dominated before the break, it seemed United would stage a comeback when it equalized early in the second half. Vidic soared above former teammates O'Shea and Brown to head home Cleverley's corner.
But shortly after De Gea blocked Larsson's sliced strike, the United goalkeeper found Borini's spotkick unstoppable as it went high into the net.
The players, like Moyes, blamed the referee.
"It's getting laughable now the decisions aren't quite going for us," Giggs said.
For Sunderland, the focus is now on topflight survival with the northeast England club four points from safety.
"Whatever it is we need to bring it into the league very quickly," said O'Shea, the Sunderland captain. "The players know we have plenty of quality, it's just making sure we use it at the right times."
The first leg of the other semifinal between Manchester City and West Ham is on Wednesday.
