Pulis calls for lifetime bans for West Brom fans
Villa won the FA Cup quarter-final 2-0, but the victory was marred by multiple pitch invasions towards the end of the game.
The Football Association has confirmed it will investigate the incidents, with reports also emerging that visiting fans were throwing seats from the North Stand.
"If that was the situation, and they've got CCTV cameras up there, those supporters should never come into another football ground," Pulis said.
"It is like people coming into someone else's house - you have to show respect.
"I am old enough to have seen isolated incidents happen like that.
"I don't want to have a go and take anything away from what happened on the pitch and what happened in the game.
"If one thing, Villa should look at the stewarding because with a game at this time of night, 5.30pm, you need to police it properly, and I am sure Villa will look at it."