Swansea manager Laudrup watched his team secure a first Barclays Premier League home win in nine games at the expense of the Black Cats on
Saturday, with three goals in seven second-half minutes helping them on the way to a 4-0 victory.
The three points moved the Swans up into mid-table; they had been sitting above the relegation zone on goal difference alone prior to this weekend's action.
Defeat for Sunderland in Poyet's first game in charge left the Wearsiders firmly rooted to the foot of the table with a meagre tally of one point from eight games, equalling the worst start to a Premier League season.
But Laudrup believes it is far too early to be writing off Sunderland and Poyet.
He said: "There are still 30 games to go, if you suddenly get two wins and six points you are right there.
"I know in this moment right now it seems very difficult for them, but sometimes you just need a little bit of luck in one game and you can win it 1-0 and you are back again.
"You see it with a lot of teams in different competitions. You can never say they are out of it.
"I always say that things are decided during the last two months of the season.
"I have never seen a team win the title or get relegated in October, November or December."
The win over Sunderland kicks off a week of three consecutive home games for the Swans, with Kuban Krasnodar and West Ham due to visit in the Europa League and Premier League respectively, and Laudrup was happy with a winning start.
"It's a big week for us," he said. "It has started well. Imagine if we get three wins this week. We could put ourselves in a very solid position in the league table and a fantastic position in the Europa League with one foot in the knockout phase.
"But we have to move on and make sure we win the next two."
For his part, Sunderland manager Poyet, once a managerial target for Swansea, has told his players they need to be mentally strong if they are to extract themselves from their current predicament.
"We need strong characters on the pitch. Players who are strong mentally," he said.
"I had watched Swansea four times this season, but I was not playing, so no matter how well I know Swansea it is up to the players to sort it out on the pitch.
"You can see Swansea have a style of play that they believe in. They played like that against Southampton, they lost that game but they kept doing it.
"They found it difficult in the first half against us, but they kept on doing it.
"That is a style and consistency you need at any level. We don't have that and we need to get that quickly."