The Uruguayan was given a stark picture of what lay ahead for him in his first game in charge of the Black Cats last month when they were trounced 4-0 at Swansea days after his international players had returned to the club.
They head for Stoke on Saturday having given their survival hopes a major boost with a fourth successive 1-0 victory over Manchester City last time out.
However, Poyet knows that will count for little if his side does not come flying out of the blocks at the Britannia Stadium.
He said: "After the last international week, it was my first game and we were destroyed by Swansea, and if we didn't learn from that and go with a different kind of approach to this game, then it's going to be very difficult to get out of the bottom.
"We need to make sure we don't repeat that and that we go with more confidence, showing how we want to play, being more competitive and make sure we get a result.
"Sometimes things happen for a reason and let's hope that that one was a good wake-up call for this Saturday."
Since the debacle at the Liberty Stadium, Sunderland's form has improved dramatically and they have won three of the four games they have played in all competitions, two of them in the league.
However, they remain deep in trouble in 19th place in the table with just seven points from their first 11 games and still three adrift of safety.
This weekend, it is the Potters and former Chelsea team-mate Mark Hughes who stand in Poyet's way, and it is a reunion to which he is looking forward, provided the result proves satisfactory.
He said: "I have got a good relationship with Hughesy. We played together and he was an unbelievable, unique player.
"He was the type of player you always want in your team because on Saturday at 3pm, he was always there, always.
"He never missed a Saturday at 3pm in terms of his desire to win football games, to score, to show the spirit that a team needs.
"For me in the beginning at Chelsea, it was important to see a player like him performing that way, caring so much on the pitch and giving you so much.
"I am pleased he is managing in the Premier League because he looks always a very special man."
Poyet has worked hard in his time in charge at the Stadium of Light to change his team's style of play, urging his players to adopt a ball-playing approach which has paid early dividends.
Hughes too is trying to instil a new philosophy after the Tony Pulis era at Stoke, and his one-time Stamford Bridge colleague knows that will take time.
Poyet said: "They have been trying - it's not an easy job. They have been playing one style for so many years and they have got players who have been there for so many years that there is a process.
"For that process, you need time and wins. Sometimes it's tricky, but I am sure with time, he is going to achieve what he's looking for."
Poyet is still without suspended duo Lee Cattermole and Andrea Dossena, but otherwise has no injury problems, although he is keeping a close eye on defender Wes Brown, who used the international break to recover from his exertions in three successive appearances after 22 months on the sidelines.
The manager said: "It was good for Wes Brown. It was very good to give him that extra little rest that probably he needed and the two and a half games in a week."