Neither side was able to find the net during the 90 minutes and despite admitting that Fulham controlled the first half, Hodgson believes that his side could easily have taken all three points.
"I thought [Fulham] were clearly the better team during the first half," Hodgson told Sky Sports News.
"But we were much better in the second half and arguably posed slightly more of a goal threat.
"We tried our best but Fulham were very hard to break down."
The draw leaves the Baggies in the relegation zone with four points from their opening six matches.