The Uruguayan succeeded Paolo Di Canio in October and has managed to lift Sunderland off the bottom of the Premier League.
However, relegation to the Championship remains a real threat with Sunderland 18th and three points from safety, albeit with games in hand on their rivals.
Regardless of whether the north-east club retain their top-flight status, Poyet believes the club require a period of stability if they are to progress.
The 46-year-old is the sixth man to have taken full-time charge of Sunderland in the last five years, but is confident he will remain at the club no matter what happens.
"It is important that we pay attention to the academy and have stability so that you don't need to keep sacking managers, paying them off, starting from zero and rebuilding," Poyet said on Friday.
"And having a sporting director and then, again, having another sporting director.
"That's how also you lose money. It's about stability. It is difficult because you have the pressure of the fans and everyone thinks you should be Champions League, Europa League, but that's not possible.
"When I took over, we were dead. Dead. Will I have failed if we go down? I will take it. I will be responsible.
"I am going to be judged from the time I came here until now. We have won more points than the games we have played since I have been here (24 points from 20 games). If we do the same now until the end of the season we will be alright.
"If we make 40 points and we go down, which means I will have got 39 points in 31 games, I am responsible. But there is a limit (to my responsibility). I will accept my responsibility, no doubt."
Sunderland, who are without a win in three league games, face a potentially crucial clash this weekend against fellow strugglers Norwich City.
