The Baggies enjoyed a strong first half of the campaign but their form has dropped off over the last few weeks after they made it to 40 points.
West Brom’s upcoming fixtures aren’t likely to provide them with easy points as they take on five of the top six before the end of the season.
Arsenal visit the Hawthorns on Saturday and Pulis is keen to see his side kick on in the hope of finishing the campaign with a record points haul in the Premier League.
Pulis said: “We’ve got some really tough games coming up now. We’ve got five out of the top six teams to play and they will be real tough challenges for us.
“I’m delighted to be on 40 points. No-one should take away what the players have achieved and what they’ve done.
“But we’ve got to try and get as many points as we possibly can and work as hard as we can to do that.”
West Brom have lost their last two but their home form has been strong this season and punters using their free bet may fancy backing them to cause an upset against Arsenal at the weekend.