The Black Cats fell to the bottom of the table over the weekend as results went against them, and the Uruguayan had threatened to walk away from the club if his side gave up in their fight against the drop.
He told reporters: "If I cannot even make a team fight for relegation, then you can think about [leaving]. If we do on Monday what we did against Liverpool then we have got a great chance so let's not give me another excuse.
"If we play the way that we played [against West Ham] then I won't go. I can't say what the gaffer (Ellis Short) is going to do. That is another situation.
"Me? I am always committed and I don't hide away from responsibility. If we go down I am going to be responsible. I am not going to say how much, but I will take my responsibility naturally."
Sunderland face Tottenham Hotspur at White Hart Lane later today.