The status of the world's oldest domestic cup competition has been brought into question recently, and has been put under further scrutiny this week with Aston Villa manager Paul Lambert claiming the majority of top-flight bosses would rather do without the distraction.
A half-empty stadium for Palace's entertaining third-round tie against Albion, despite the Black Country club offering cut-price ticket incentives, only seemed to suggest fans are also voting with their feet - although 2,000 Palace supporters made the trip to the Midlands.
Pulis' men progressed to the fourth round after Dwight Gayle fired them into the lead midway through the first half before substitute Marouane Chamakh put the icing on the cake with a tap-in deep into injury-time.
The sides last met in the Premier League when the Baggies beat Palace 2-0 in early November at The Hawthorns, in a game which attracted a crowd of 26,397.
"There's got to be some way of filling stadiums up, especially for third round and fourth round ties at Premier League grounds," Pulis claimed.
"That has to be looked at because it is a wonderful competition.
"For all of what is going on, we've got to try as a nation to make sure we keep it a great competition by filling stadiums for games - that's certainly a help."
Concerned for the status of the competition, Pulis urged the FA and football clubs to find a way of promoting the FA Cup and increasing gates across the country.
"It's difficult because it's just after New Year, people have spent a lot of money, so you understand that," he added.
"But, as I said, there's got to be a way at this time of year that clubs can attract full houses, how they do it you'd have to ask chief executives."
Palace will discover their fourth round fate on Sunday afternoon before returning to Premier League action with a trip to White Hart Lane to face Tottenham next Saturday.