The Swans conceded an injury-time equaliser in their 1-1 Europa League draw at Kuban Krasnodar on Thursday, and have won just one of their last five fixtures in the English top flight - a run that includes last Sunday's 1-0 defeat to South Wales rivals Cardiff City.
With Swansea having taken maximum points from both home fixtures against Stoke since their promotion in 2011, Laudrup knows his side need a positive result again this time around, though he is not helped by the fact that last season's top goalscorer, Michu, may be sidelined for up to a month with an ankle injury.
"The game on Thursday was the first game after the derby so that was always going to be special," he told The Daily Mail.
"But Sunday is the next game in the Premier League. So a combination of that and the fact we play at home makes it a game that we have to get a result.
"The players are well aware that we have to perform exactly like we started on Thursday and play in the same way.
"The game will be different because Kuban were a team who really wanted to wait for us and played counter-attacking football.
"But Stoke is a different team. They are very strong and powerful, but we have to play to our best and play them like we did last year (a 3-1 home win in January).
"We put them under pressure, kept the ball and tried not to give them too many set-pieces because they are very strong in that department."
Swansea currently sit 13th in the Premier League with 11 points from 10 games.