The Palace manager inspired his team to only their third away win of the season in all competitions and in turn extended his own personal unbeaten run at The Hawthorns to seven games.
Pulis admitted being drawn against another top-flight side made for a difficult third-round tie, but praised the attitude shown by his players to progress in the competition thanks to goals from Gayle and Chamakh.
"It was tough coming to a Premier League club away from home," said Pulis. "It was always going to be a tough tie. West Brom did well in the second half.
"We defended with our lives at times. We created some very good opportunities and some good chances.
"We were disappointed we didn't score a few more. When we brought Chamakh and (Jason) Puncheon on we looked better. Chamakh is a top player."
Pulis singled out goalkeeper Julian Speroni for special praise after the Argentine kept them in the game with crucial saves, particularly to keep out Matej Vydra's volley just after the hour.
"It was a great save (from Vydra)," he added. "But that's what you pay him for or you're hoping he'd do things like that.
"There were a lot of saves around his body. The one save that we're talking about was an outstanding save.
"He's been a top goalkeeper at the football club for a long time."
