The Swans have suffered back-to-back domestic defeats from testing fixtures against Manchester United and Tottenham, and sit bottom of the table.
They also lost the second leg of their Europa League play-off tie 2-1 against Petrolul Ploiesti in Romania on Thursday.
Although the Welsh club still progressed to the knock-out stages of the competition 6-3 on aggregate, Laudrup was unimpressed by their display.
Not for the first time, the Dane laid the blame for the loss on his side's inability to make the most of several good chances, and he knows their profligacy in front of goal must end as they look to get on the board at the Hawthorns.
Laudrup said: "In Romania we had the luxury of a 5-1 lead to fall back on. When we play in the league we do not have that. Every game is just a one-off.
"So we have to be better in this area. You do not get eight chances away from home, whether that be in Europe or in the Premier League.
"We have to be much sharper on Sunday when we have these possibilities."
Laudrup is keen to add a striker to his squad before the transfer window closes on Monday, with Peter Odemwingie and Alvaro Vazquez on his radar.
But with Wilfried Bony absent in Romania with an ankle injury, and Michu being fielded in his preferred attacking midfield role, Laudrup opted to hand a first start to Rory Donnelly.
The Northern Irishman failed to take two presentable opportunities but showed some nice touches, and Laudrup praised the 21-year-old's performance.
"He did fantastic, I only told him he was playing a couple of hours before the game," he said.
"It was a big thing for him to come in and play in the first XI in a game in Europe and he did very well."