Chris Coleman admits Jason Steele will be "disappointed" with Middlesbrough's second goal and the Black Cats boss didn't think it was a foul on the goalkeeper.
The former Boro stopper was handed a first start under Coleman after impressing in training, with Robbin Ruiter on the bench for the game at the Riverside.
Sunderland fell behind to a 10th minute Rudy Gestede goal, the striker played in by a superb through ball from Adama Traore, before slipping the ball past Steele who had rushed off his line.
And they scored a decisive second three minutes before half-time, Steele failed to deal with Stewart Downing's corner, the ball bouncing around before Martin Braithwaite hammered home.
There were appeals for a foul on Steele, under pressure from Gestede, but the keeper didn't make any meaningful contact with the ball.
Coleman didn't believe it was a foul and said referee Chris Kavanagh made the right decision.
Steele made a couple of important saves after the break but the damage had already been done, with the Black Cats out of the cup at the third round stage.
On the second goal, Coleman said: "I didn't think it was a foul. Sometimes you see them given but if I am being honest I think keepers are protected a lot.
"I can't say it was a foul because I didn't think it was. The big fellas pulled off one or two saves for us. The second goal killed us before half-time.
"He has come to punch it and I think the referee got that right. I can't criticise the referee for that."
"It was hard for [Jason] to come in. If you are looking at the team in front of him, we are stretched, we are low in central midfield, we were playing Willo [Marc Wilson] in central midfield who is a centre back and young Ethan Robson in his first game, who I thought did very well. I was very happy with him.
"We are stretched though and always would be.
"Steeley will be disappointed with the second goal, for sure. Other than that, his kicking was okay and he pulled off one or two good saves."
When asked whether Coleman felt Steele should have come out for the first goal, the manager added: "I would have to see it again. I have only studied the second to see whether it was a free-kick or not.
"I saw it in real time but couldn't comment on that unless I see it a second time."
On the game itself, Coleman added: "Coming here, before we have kicked a ball we knew we were up against it. We have to be a bit realistic.
"Saying that the two goals we gave away I was disappointed with. To a point in the second half we did some good things, we lacked some belief in the final third.
"You want one of those chances to go in, Josh Maja hit the bar and Randolph produced a fantastic save [from Tyias Browning]."
"Boro are a good team, they have a good manager and will be there or thereabouts. For us to come here with 11 missing it was always going to be tough.
"I thought we had some spirit though, I won't criticise them for lack of running or effort. Lack of belief perhaps but it is what it is. We are out of the FA Cup and lost to our local rivals, of course it is disappointing.
"We have taken a shed load of fans again and not put a smile on their faces. I knew it would be tough. I was pleased they didn't fold."