The Uruguayan has acknowledged the progress the club has made since his arrival in October last year but has warned there is still work to be done to avoid relegation
The Stadium of Light outfit could climb out of the relegation zone, on a temporary basis at least, with victory over Southampton in Saturday's early game, having moved off the foot of the table with a 4-1 win at Fulham last weekend.
However, Poyet has warned his side their job is only half done.
"It would be normal to start relaxing, but it is our job to stop them doing that," the Uruguayan told reporters.
"I don’t want to be negative and say that we have done nothing because that would be wrong. That sounds negative, and that is not the case.
"But I would like to say that we have only done half of the job we have to do. We are halfway there, but if we don’t do the other half, it will count for nothing.
"We were very far away when we started this, and everybody was looking at the table and writing us off completely. Now we are there in the mix, but that is still only a job half done.
"We have to speak strongly in those terms, because completing the first half was difficult, and achieving the second half is not going to be any easier."