But Robinson told Sky Sports afterwards that he expects to hang on to his job for the remaining autumn internationals against South Africa.
Asked if he intended to be in charge for next Saturday's clash with the Springboks, replied: "Yes, I think I am going to be there".
Robinson, asked if he thought the powers that be within the Rugby Football Union would stand by him, replied "yes" again.
The England coach had initially baulked at the suggestion that he it was time for him to go, responding with a curt: "I'm not here to answer those questions. It's not for me to discuss and I'm not making that decision."
Pressed further, he snapped: "If you want to discuss the game we'll discuss the game. If not we'll finish (the interview) now. It's your choice."
On England's abject performance, Robinson added: "Obviously we're very disappointed with the result. Credit to Argentina, they performed well today but there were a lot of errors from us.
"We turned too much ball over and kicked too much ball away. There were a lot of individual errors, turnovers at the tackle area, which allowed Argentina into the game and gave them momentum."
Robinson defended his decision to take off fly-half Charlie Hodgson and give an England debut to Toby Flood, whose loose pass led to an interception try from Federico Todeschini.
"Toby was our replacement number 10 and we felt we needed a bit of direction from him. I thought he did some good things when he came on."
If Robinson does remain in charge for Saturday's clash with South Africa he will have to find some way of lifting a dispirited England side but he would not be drawn on whether or not he plans to make wholesale changes.
"We need to give ourselves a bit of time to think it through before making important decisions as we prepare for the South Africa game."