His contribution came 13 minutes after United skipper Nemanja Vidic had dragged the visitors back into the game with a bullet header which cancelled out Ryan Giggs' own goal in first-half stoppage time.
The Welshman could only turn former team-mate Wes Brown's cross into the net under pressure from another old boy Phil Bardsley on a night when United enjoyed plenty of possession, but could not make the most of it.
The Black Cats have now won six cup ties this season and only three Barclays Premier League games, and they have beaten Newcastle, Everton, Manchester City, Chelsea and now United while succumbing to less taxing opposition.
Poyet said: "That is something I need to find out, why we are capable somehow of beating top teams and to be so clinical in the cup, and we cannot do the same in the league.
"Analysis is part of my job, so I am going to keep looking at different things that we are doing in the cup. It could be the opposition, it could be how high you defend, it could be the mentality of the group of players...
"I need to find the reason because if not, something is happening, it's mental. But I need to find that reason."
But when he was asked who were favourites to reach the final, the Uruguayan replied: "No chance. Manchester United, with probably Rooney and Van Persie coming back in two weeks' time?
"Where we are is in a better situation because we won the first of the two. But playing Manchester United away, anything can happen, so we need to make sure we put in another very good performance."