Pulis was appointed as the Baggies boss towards the back end of the last campaign, but his impact at the Hawthorns has not been as great as it was at previous clubs.
Although West Brom avoided relegation last term, and are currently sat in 13th place this time around, Thompson is worried that they could fall into trouble if they start conceding goals.
"I fear for them," Thompson admitted. "West Brom are keeping clean sheets, but they never look like scoring goals. It doesn't look like there's anything happening.
"I think some of the players are losing their faith in some of the tactical nous that Tony Pulis is bringing. You know, and you hear things, and there's players in there that for a while will do things. But then when they start losing faith, and they don't go into the positions they are expected, if they start conceding goals, you'll see them slip greatly.
"I am worried for this West Brom side."
Pulis' strength has always been his ability to organise a side, but the lack of attacking quality West Brom have shown this season has frustrated.
Despite the additions of Rickie Lambert and Salomon Rondon, the Baggies have still looked toothless up front, and they have struggled to create chances.
West Brom have scored just seven times over their first nine league matches this term, and frustration is starting to mount at the lack of entertainment on display.
The Midlands outfit did win their last match against Sunderland, though, and they will hope that victory will be the one which kick-starts their season and allows them to piece together a positive run of form.