The Scotland international, whose stunning 16th-minute volley had fired the npower Championship visitors into the lead at the Stadium of Light, played a part in substitute Fraizer Campbell's 59th-minute equaliser when his loose pass set James McClean away on a pacy counter-attack.
Robson's error did not prevent him from picking up the man of the match award at the end of a pulsating fourth-round encounter, but manager Tony Mowbray revealed that proved little consolation.
Mowbray said: "He came in and he threw his champagne in the bin.
"He is a very emotional boy, Barry, and yet he epitomises the spirit required as we as a club move on.
"Particularly in the Championship, you have to fight your corner every minute of every game, and Barry Robson leads from the front in that aspect.
"He also has a left foot like we have seen. If you were there against Hull a month or so ago, he rifled one in the top corner from 35 yards with his left foot.
"Today, he scored a great first-time volley. He has the quality, as well as a heart the size of a lion, to help drive us on this season."
Boro arrived at the Stadium of Light on the back of a three-game losing run in the npower Championship, but went ahead through Robson's fine volley.
Sunderland thought they had levelled six minutes before the break when Craig Gardner fired home off the inside off the post, only for a controversial offside flag to ruin his celebrations.
Manager Martin O'Neill said: "I have been told it was given for offside, and it wasn't offside.
"The referee is adamant that's what the linesman gave it for. There is supposedly a suggestion of handball beforehand, which I don't think he saw.
"I said to the referee at half-time, 'Was it handball or offside?', and he said, 'I never mentioned handball', so if it was given for offside, it should have stood."
Mowbray was similarly puzzled, if less disappointed, by referee Kevin Friend's decision.
He said: "Martin had a very similar view to me and I'm pretty sure he wouldn't have known what on earth that goal wasn't given for when he sees the linesman's flag up."
Boro striker Lukas Jutkiewicz passed up a glorious opportunity to give the visitors a 2-0 advantage in the final minute of the first half, and former Manchester United frontman Campbell provided the finishing touch to McClean's 59th-minute cross to claim his first goal since April 2010.
O'Neill said: "I am really, really delighted for him, and I think everybody is around here - it's hard not to be with the injuries he has sustained.
"He took it brilliantly as well - it may well have been his first or second touch."
However, the draw came at a cost for the Black Cats, who will send skipper Lee Cattermole, who missed out with a hamstring injury, and defender Wes Brown, who suffered suspected medial ligament damage, for scans.