It seemed already hard for West Brom to come out of relegation. Although will give some appreciation with the way they were playing lately but that was something that they should have shown earlier and not in later stages when the situation already had turned towards worse for them.
As for Arsenal, it is another top 10 finish likely this season. They need to be consistent with their performance if they have to finish on a better place next season. Consistency is what bringing Arsenal down.
With this loss vs Arsenal, West Brom will be relegated since it is impossible to catch 17th place team who are 10 points ahead. While, there are only 3 games left for West Brom's season which is max 9 points if they win all of them. With regards to Arsenal, being in top 10 in the prem isnt enough of an ambition for a club that craves Champions League football. Arteta is doing a decent job at Arsenal..but im not sure decent job cuts it for them. They will probably stick with him for another season and see how it goes. Premier league has been very competitive this season(other than Man City, who have been blazing, and the relegation fodder).