Brown Ideye scored twice while James Morrison and Saido Berahino also netted as the dominant Baggies romped to the win at The Hawthorns on Saturday.
Morgan Amalfitano was also sent off for West Ham just 10 minutes after coming on in the second half.
Pulis has lost just once in his first eight games since taking charge at Albion in January and they are also four points above the relegation zone in the Premier League.
And he said he is working on his team’s strengths after they moved into the FA Cup quarter-finals.
“This team has different strengths to what we had at Stoke and Palace,” he said.
“On Wednesday against Swansea, you think it was showing a bit of fruition. There’s still a long way to go; we have to keep our feet on the ground and look at it from there.”
Pulis also insisted he will be looking to progress to the semi-finals of the FA Cup, not put out a weakened side in view of the Premier League survival battle.
“Whatever draw we get, we’ll be putting a strong side out to get through,” added the Albion boss.