Saturday's loss at The Hawthorns has left the Gunners five points adrift of the Premier League's top four with 11 games to go.
Arsenal have finished in the top four for 20 consecutive seasons, but this season there is the real risk that Champions League qualification may be beyond their reach.
Wenger told reporters after the game: "It was a tough performance. They caught us on set-pieces and one break and that made the difference.
"We didn't create enough. We lost Sanchez in the second half, he was very dangerous in the first. He came out in the second half and he couldn't move any more. In the first half he was a guy who created a lot.
"It leaves us in a unique situation that we've never had before. We face big problems to regroup and find resources to sort out the problem. We need some togetherness. We face some serious challenges. The City game at home is a big game for us."
Arsenal welcome Pep Guardiola's Manchester City to the Emirates Stadium on Sunday, April 2.