The Black Cats looked on course to record a priceless win in their relegation battle with a shock victory over City, before Samir Nasri's 88th-minute equaliser trickled over the goal-line following an error by the Italian.
Poyet's bid to steer the club away from the drop zone gets no easier, with a trip to Chelsea on the horizon, but the Uruguayan insists that he has no intention of dropping the shot-stopper for the test with the Blues.
"I think Vito wants just to play again as soon as soon as possible," Poyet told reporters. "I have got no doubts he is going to play, it's not a problem for me.
"That's why when you have a son, the first thing you say is, 'Don't play in goal. Any position but in goal'.
"It doesn't matter how well you play for 89 minutes, it doesn't matter how many saves or crosses you catch, if you make one mistake, it is going to cost you a goal."