The Baggies were drawn away at League Two side Accrington Stanley in the second round of the competition and cruised to a 3-1 win on Tuesday night.
Pulis previously led Stoke City to the FA Cup final in 2011, where Manchester City claimed a 1-0 win at Wembley, and the Welshman is eager to bestow the same experience upon his current side.
"We've taken the competition seriously," he told BBC Sport after the game at the Crown Ground. "It gives us a chance to get to Wembley.
I've been fortunate to take Stoke there and it would be lovely to do that with West Brom."
The draw for the third round of the competition will be made this Thursday in Beijing, at 4.15am BST.