Craig Gardner had given the bottom-of-the-table Black Cats an unlikely lead after Phil Jones and Nemanja Vidic between them failed to deal adequately with Emanuele Giaccherini's driven cross, and it was one they deservedly held until 10 minutes into the second half.
United got themselves back into the game when Adnan Januzaj expertly drilled home Patrice Evra's low cross, but the teenager's second finish was even better as he thumped a left-volley into the bottom corner after John O'Shea's 61st-minute headed clearance dropped to him.
The Black Cats have now collected just one point from a possible 21 this season and when asked if he felt the players were playing for him, Ball said: "The players are fighting for themselves - they need to fight for themselves as well.
"What I mean by that is they need to work hard for each other, and they know that. I will demand that from them and I would expect them to demand it from themselves.
"If people feel that's because of me, that's fantastic. But it's not about me, it's about the players in this club and it's important they do work very, very hard to give themselves the best chance of getting the results."