The Gunners succumbed to their fourth defeat in five Premier League matches at The Hawthorns to leave their hopes of Champions League qualification in the balance.
"We're bitterly disappointed. We're sorry to the fans. That's not acceptable for Arsenal Football Club," Oxlade-Chamberlain told Sky Sports News.
"West Brom made it really tough and defended really well. We knew who their danger men were and we failed to stop them."
The result has seen a five-point gap emerge between fifth-placed Arsenal and the top four of the Premier League, with Everton snapping at their heels.