Poyet only took charge at the Stadium of Light in October following the early-season sacking of Paolo Di Canio, but the former Brighton boss is in danger of presiding over Sunderland's relegation to the Championship.
The Uruguayan has spoken to Short regarding the club's plight at the bottom of the table and he is not concerned about his job being under threat.
"The message from the owner is support, total support," said Poyet. "I spoke to him this week and he totally supports [me].
"He made a decision and he is standing by it until the end.
"The conversation was very natural. I don't need to tell you what we said to each other, but it was natural and straightforward.
"We spoke about the situation and why we decided to stick together until the end."
Sunderland embark on a run of three tough fixtures in a week at home to Everton on Saturday and sit seven points from safety.
The Black Cats do have two games in hand on their relegation rivals, but Poyet acknowledged his side need a 'miracle' to stay up, with trips to Manchester City and Chelsea to come on the back of facing Everton.
He added: "If the situation were impossible I would say [it is] impossible, but I am saying we need a miracle.
"A hypocrite would say 'miracle' meaning 'impossible', because they would use the word as a way of not speaking the truth. I am not like that. I am telling the truth. If you want me to lie, I cannot do that.
"I care. That's the way I have been all of my life. I become supportive of whichever club I am at.
"As soon as I sign a contract for a club, that's my club. I'd die for that club. That attitude has helped me to create a relationship with the club and its fans.
"I am not a hypocrite. We have too many hypocrites around the world, telling people what they want to hear. I am not going to be like a politician.
"If one of my players thinks I shouldn't be negative then he doesn't deserve to be a Sunderland player. If one of the fans thinks I should be lying to them then I should not be here.
"I keep saying to the fans, trust us to the end, until the last game, the last goal, then we will talk. Then we will be open, we can talk about everything. There's no point analysing now because you can't change anything."