Long-serving manager Arsene Wenger was again the subject of fan protests asking for him to stand down, with a clutch of banners appearing in the away end after Albion defender Craig Dawson headed his second of the game 15 minutes from time.
Alexis Sanchez cancelled out Dawson's opener as early first-half goals were traded, but West Brom hit the front again 10 minutes after the break as substitute Hal Robson-Kanu made an instant impact.
Arsenal are five points shy of Liverpool in fourth, with their hopes of UEFA Champions League qualification dwindling on the back of four defeats from their past five top-flight games and England midfielder Oxlade-Chamberlain knows a turnaround is needed quickly after the international break.
"We need as many three points as we can get. We're bitterly disappointed and we're sorry to the fans," he told Sky Sports.
"It's not acceptable for Arsenal football club to lose in the way we did today.
"I'm not sure it's going to get any easier so we've just got to battle our way out of this."
Oxlade-Chamberlain felt Arsenal were in control after their early setback, but was aghast that they let the contest slip away after the interval, while injuries to goalkeeper Petr Cech and top scorer Sanchez compounded their misery.
"We're very disappointed," he said. "Obviously in the first half I thought we were very comfortable and just needed to be careful of them on the counter-attack and from set-plays.
"They scored from the set-play, but we equalised quite quickly and we controlled it.
"Second half they pressed us higher and it was a lot harder for us. The second goal was disappointing, it was a bit scrappy and we've let ourselves down then."