Poyet, appointed earlier this month by the struggling Wearsiders to replace the axed Paolo Di Canio, pointed to Swansea's progress under the former Danish international as a benchmark for his own foray into Premier League management.
Former Chelsea and Tottenham defender Poyet cut his managerial teeth in League One (third tier) and the Championship (second division) with Brighton and Hove Albion before he was dismissed in June for an undisclosed breach of club discipline.
"I suffered against him more than play against him because he was outstandingly gifted; he was an incredible football player," Poyet, who played against Laudrup in Spain's La Liga, told the Sunderland website (www.safc.com) on Thursday.
"You can see now that he is trying to impose that quality that he had naturally on his team. They did something unique last year for a team like Swansea by winning the (league) cup and being in Europe.
"They keep progressing, it's a club that is going in the right direction and has been for many years."
Poyet has inherited a Sunderland side who prop up the standings with one point from seven games.
Having earned a reputation for getting his Brighton side to play attractive attacking football, Poyet said Sunderland needed to go back to basics to dig themselves out of their current predicament.
"First we need to start doing the right things; not conceding goals, keeping the ball better, creating chances - winning football games really.
"I am convinced that if we start getting results and we start getting better then sooner or later we will see a totally different approach.
"I'm sure that the fans are going to really enjoy watching the team."