Two second-half braces by Wilfried Zaha and Christian Benteke and an own goal by Darnell Furlong helped the Eagles cruise to what in the end was an easy victory against a side sitting in the relegation zone.
It was also a result that moved Palace up to 11th in the Premier League on 16 points after 11 games.
On the second haIf
After the game, Hodgson acknowledged that as the game went on his team's tempo and intensity got higher.
"I thought the first half was okay but it was important in the second half that we didn't use the fact that they would want time and space.
"I wanted the midfield to slow things down and to just be content and to keep the ball. It was important we kept it with a view to getting it forward and to getting it to our final third.
"In the final third, with the runs and the combinations that we work out as a team and I thought we saw that today. The tempo and intensity of the game got higher over the course of the game."
On Wilfried Zaha's showing
Zaha, who played his first game since testing positive for Covid-19, clearly showed what his side have been missing in his absence as his two goals and one assist were huge factors behind Palace earning all three points at the Hawthorns.
When speaking on the 28-year-old Hodgson revealed that this season goalscoring is something that he feels that Zaha has added to his game.
"I see it from Wilf all the time and I see it also in training. We know that he has that ability when we can get the ball to his feet in the final third.
"He is very very difficult to stop because he can twist and turn both ways. "
He has got excellent feet, excellent ball control and of course what he is added to his game this year or what he certainly has worked hard to add to his game is his goalscoring.
"He is always looking to get shots away. That first goal, I often see that in training, it is not a fluke. The second one is his determination to get to the ball after Eze's excellent run.
"Also that was a goalscorer doing that so if Wilf can keep that up it bodes very very well for us.
Hodgson added: "He was a bit disappointed that I took him off with 10 minutes to go because he wanted a hat trick but that is a good sign too.
"I would have been less happy if he had said I was quite content to come off, I do not need the third."
Along with Zaha, Benteke also grabbed a brace, both of which came in the second half, and this was as many as the forward got in the 24 Premier League games in which he featured last season.
Hodgson said that he has shown a glimpse of the reasons why the Eagles brought him from Liverpool back in 2016.
"I would like to think that he is going to get lots of plaudits for his performance. It is not just his goals. There were other aspects to his play which were good.
He has waited a long time. He has been on the bench a lot this season so far without actually getting in and showing what he can do and that is even going back to the lockdown period.
"So he has been patient and he has never stopped working to be fair to him and today he showed the type of player he was when Palace brought him from Liverpool.
"He showed once again to everybody out there that he has not lost it. He is still Christian Benteke, you can still rely on him and he has now to got to keep that going.
"The thing about players' performances, they need to be consistent. The two players mentioned (Zaha and Benteke) have had good games but I need them to have good games in the next three coming up as well.
"That is the real test. That consistency and that reliability."
On competition in the squad
Hodgson admitted that he will have selection headaches going forward into future games.
"I know what we did today we have in us, and I know that we have that quality. I know now that we have a lot of competition for places and that is going to give me many many headaches.
Many sleepless nights really wondering what is the best combination of centre backs. Who are the best full backs. What midfielders should I choose and front players from these four good ones should I actually use.
"But I suppose that is the sort of headache that top clubs have all the time with their side, it is just something that I have not been 100% used to during my three and a year half at Crystal Palace."
On the red card
West Brom ended the game with ten men after Matheus Pereira was adjudged by referee Paul Tierney to have kicked out at Patrick Van Aanholt in the 34th minute.
Hodgson said: "It seemed to me quite close to it that the player kicked out and the referee was there close enough and redeemed that the player made contact.
"It is never nice to see one of your players sent off and not even nice to see opponents sent off necessarily for those things, but unfortunately if one of your players does it and is seen to do it I am afraid that they have to pay the price."