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The 47-year-old head coach this week took the unusual step of issuing an open letter to fans after demoralising defeats to QPR in the Barclays Premier League and Sky Bet League One Bradford in the FA Cup fifth round had been misinterpreted.
Poyet finds himself in a difficult position heading into Saturday's crucial home clash with West Brom, with the Black Cats having slipped to within two points of the relegation zone in which they were entrenched for much of last season.
However, he insists he thrives under the pressure.
He said: "I like pressure because it's the way I have been brought up
When you are in Uruguay and when you play football and when you play for the national team, the pressure is there to win.
"There is no other result, so it is part of my life.
"Can I work without pressure? I don't know - I have never done it so far
I have never played football or managed without pressure.
"I suppose it would be nice, but maybe I would not be myself after because I don't have the pressure.
"I don't know
It's part of the game
I like it, I really like it."
Poyet remained coy over his team selection as he conducted his pre-match press conference, revealing that both key midfielder Lee Cattermole and January signing Jermain Defoe could be involved, but going little further
But he hinted that he might gamble on striker Defoe, just as Atletico Madrid boss Diego Simeone did, ultimately unsuccessfully, with Diego Costa ahead of last May's Champions League final.
He said: "Last season's Champions League final, Costa played 20 minutes
You would think if there's a game in which you need a player like Costa on the pitch, it's that game.
"Then when he comes off after 20 minutes, it's very easy to say that he shouldn't have played.
"But that's too late."
West Brom boss Tony Pulis expects Poyet to send his Sunderland side out firing.
While West Brom's form has started to pick up since Pulis took charge early in January, the Black Cats have hit a potentially damaging slump.
The Wearsiders have won just one of their last eight league games and are only two points above the relegation zone in 15th place.
With five wins and just one defeat in eight games in all competitions under Pulis, West Brom appear to be heading in the opposite direction
But the head coach will take nothing for granted at the Stadium of Light this weekend.
"We have watched them on two or three occasions," said Pulis, whose side are two points above Sunderland in the table.
"We watched the QPR game and in the second half they could have scored two or three goals
They had a sloppy first half then Gus looked at that
They really pulled it together and if they had got the breaks they could have easily got a result.
"They are not far short of getting results
I have tremendous respect for Gus and that football club, so we will be prepared for what will be a tough battle."
Pulis would not necessarily be drawn on the issues concerning Poyet and the supporters, but is convinced the former Chelsea midfielder is a strong enough character to turn the situation around.
He said: "Gus has got to do what Gus has got to do
We are all different
What Gus does is up to Gus and you have got to give him the respect he deserves as a tremendous player, while he has coached and managed and done very well.
"He took Sunderland to a cup final last year, so he hasn't done too bad.
"He is straight as a die, whether you talk to him on the pitch or off it
He is a good football man, he knows the game
I have enjoyed his company when I have been with him.
"It is a wonderful area - the north east is a very passionate area for the clubs.
"The expectations are high up there and you have to live with that
Gus has been up there 18 months, two years, he will understand that now."
Source : PA
Source: PA