The Irishman looked on as his team turned in a dreadful opening 45 minutes to trail 1-0 to Simon Davies' free-kick.
And the visitors' lead could have been greater had David Healy not fired wide of an open goal.
However, Keane's half-time team talk was rewarded with a spirited fightback. Kenwyne Jones headed home his fourth goal for the club and his third in as many games four minutes from time to claim a draw.
Indeed, had keeper Antti Niemi not blocked substitute Anthony Stokes' injury-time shot, the Black Cats might have ended their three-game losing run in the Barclays Premier League with a victory, something which could not have been further from their thoughts at the break.
Asked if he was relieved to have got a point or disappointed not to have won the game despite Greg Halford's second dismissal of the season, Keane said: "I'm not sure.
"I'm a bit confused at the moment. I don't know if I'm happy or sad or frustrated.
"But it's funny, when you are a goal down at home with 10 or 15 minutes to go and you are down to 10 men, we will probably look back and say it was a point gained rather than two dropped.
"It was vital we got something out of the game. It would have been fantastic to have nicked it at the end, but the players earned the right.
"They keep going - the fans were different class today, they kept them going.
"It was a strange day."
Fulham boss Lawrie Sanchez left the north-east once again bemoaning his side's inability to hang on to a lead.
He said: "We are extremely disappointed. There was only one team should have won the game and one team who looked as if they were going to win the game. Ultimately, we were done five minutes from the end, which is disappointing having dominated.
"But for Antti's save at the end, we could have gone home losers, which would have been a gross injustice. But that's football, that's the way it is."