It is the first time Allardyce has been relegated in his long management career, and he will now sit down with the Baggies to discuss whether he will stay at the Hawthorns for next season.
"It's too early to talk about that," he said. "For me, it's about getting over the disappointment and when the time is right I'll talk about what's going to happen next season.
"At this moment in time, it's not a question I'm prepared to answer."
"Then in five minutes of sloppiness, Arsenal showed the quality of finishing we couldn't find. In the second half, instead of going under, we came out fighting.
"We had to wait for an absolutely brilliant goal by Matheus Pereira yet we had much better opportunities than that one. We had chances to convert and didn't do it, and that's probably been the most disappointing thing over the last 14-15 games - it was so near yet so far.
"Then right at the end we saw the difference in quality between the two sides with the free-kick which put them 3-1 up.
"I thought that was a bit flattering for them on the basis of the whole 90 minutes but it's something we've been suffering from for a while. While performances were good and I couldn't ask for too much more from the players tonight, it wasn't quite good enough."