The Baggies were strongly linked with a move for the France international when it became clear that Manchester United were prepared to sell, but the 27-year-old chose to join Everton in a £20m deal.
West Brom boss Pulis has said that he was frustrated to miss out on the central midfielder, but has vowed to continue searching for fresh blood in the January transfer window.
"We're trying to get a level of player that will improve us. He's gone to a club that have finished in the top seven for the last few years and play in front of 40,000 each week," Pulis told reporters.
"After Morgan there was still money to go for others as well. We've got people we'd like to bring in, whether we can is another matter. It's a small pool we're fishing from. I don't want to get into a situation where there's a lot of players here and you don't know how good they are."
Schneiderlin's move to Everton could end up costing the Toffees £24m.