Chances were hard to come by but the Black Cats were grateful to Bramble for a superb block in the last minute of injury time which prevented Danny Graham getting a clear shot on goal.
"I have to say it was a fair result," O'Shea told Sky Sports 2. "Swansea had two of the clearest chances.
"We could have been better going forward and both teams cancelled each other out, but it was a great tackle from Titus which stopped Graham getting the winner."
Asked if he had been concerned when striker Itay Shechter had gone down under his challenge in the area in the fifth minute, O'Shea added: "No, I think a few times before that he had gone over fairly easily so I think the referee had that in mind so I wasn't concerned too much."
Swansea boss Michael Laudrup was quick to absolve referee Andre Marriner of any blame.
He said: "From the bench when I saw it, it didn't seem like a penalty to me, but after I saw it on television, it did.
"But then again, it's so easy for us, isn't it? We have two, three, 10 times to see it and then we decide if it was or wasn't.
"The referee has only two seconds, so I am really not complaining."
Swansea captain Ashley Williams said: "It's a tough place to come and I think we played well and stuck to our game plan.
"We nearly nicked it in the end but a draw is a fair result. We are happy with a draw to be honest."
Sunderland manager Martin O'Neill admitted his side had been far from their best.
"We didn't play very well at all, the point was about as much as we deserved," O'Neill said.
"We had no game at the weekend and I thought that would help us immensely, we rested up and got ourselves prepared.
"I thought Alfred (N'Diaye) was a little bit lost, overall we were second to the ball and allowed Swansea to dictate the pattern to the game and at home that wasn't good enough."
Laudrup was disappointed not to claim all three points, but was pleased with the response after reaching the Capital One Cup final with a 2-0 aggregate success over Chelsea last week.
"In the first half we dominated completely, the only but was that we did not score," Laudrup said. "Second half was a little more 50/50 but without being dangerous.
"We had two huge chances with Nathan Dyer and in the last minute with Danny Graham, so maybe we should have won the game but my players' performance was a great reaction after the second leg against Chelsea.
"We play away against a good side and I didn't see one clear goal chance from Sunderland."
Asked about the penalty claim, Laudrup added: "From the bench it didn't seem a penalty and after seeing it again I think there is contact but the referee has one or two seconds to decide. I think it was a penalty."
As for the future of Graham, he added: "I really don't know. Sometimes when we are asked these questions, we have to be like politicians and avoid the answer.
"But in some part it's because we really don't know what is going to happen.
"We have already seen some examples during this January transfer window where other clubs have had players that were quite sure to go to one cub and then suddenly, they show up at a press conference with another shirt on.
"My answer to that is that when we answer - I think I can say 'we' for a lot of managers because we don't know 100% what is going to happen in transfer windows."
Sunderland boss Martin O'Neill was on Tuesday awaiting the outcome of his club's bids for strikers as the winter transfer deadline fast approaches.
O'Neill revealed after the 0-0 Barclays Premier League draw with Swansea, in which prime target Graham might have snatched victory for the visitors at the death, that the Black Cats had made "a couple" of offers and were hoping for a breakthrough before Thursday's deadline.
He said: "We have made bids for a couple of players, but we didn't make them overnight, we made them some time ago.
"Of course, it's absolutely the prerogative of the team to whom we have put these bids in either to accept or not accept as the case may be.
"We wouldn't be the only club in that sort of position, this idea that we are waiting until January 31.
"There may be a host of signings in the next 48 hours, I don't know, but there's every possibility because that seems to have been the way of it in the last number of years."
Sunderland's interest in 27-year-old Graham has been well publicised despite O'Neill's refusal to acknowledge it publicly, but his appearance as a second-half substitute was booed by sections of the home crowd, a reflection of his Geordie roots and his comments about their club in a fanzine interview.
But O'Neill said with a smile: "I think he is himself reportedly a Newcastle fan, so I think the reaction to that was probably quite a natural reaction.
"But Bob Stokoe was looking down at him."
Swans keeper Gerhard Tremmel had only one save of note to make from Sebastian Larsson's first-half free-kick, and although opposite number Simon Mignolet was little busier, Nathan Dyer passed up a glorious opportunity before Graham's big moment.
O'Neill said: "We played very disappointingly in the game. Coming on the back of a couple of great wins, I thought we were going into the game with plenty of confidence, and also with the weekend off, I thought we would be refreshed and really ready to go.
"But other than a spell just after half-time for a while, I thought Swansea, possibly without looking all that fantastically dangerous themselves, really dictated a lot of the game."