Arsenal have qualified for the Champions League for 15 consecutive years but that famous record is increasingly under threat after another Premier League defeat left them trailing Chelsea in third and Tottenham Hotspur in fourth – and with Everton above them in fifth.
"We have lost two big games in the last week," said Wenger, referring to the previous Sunday's 2-0 home loss to Manchester City.
"And that is very damaging for us. We cannot afford to drop points any more if we want to be in the top four. That is a concern. It is very damaging for our position in the league and it is difficult to swallow."
The Arsenal manager claimed the loss was down to another slow start and the pressures of fixture congestion, which have left his squad tired and jaded.
"It was similar to last week," he said. "The team has fantastic quality and spirit, but we come into the game when we're 2-0 down. At the moment, that's worrying. In the big games, once you start 2-0 down, it's very difficult.
"We had a physical problem to get going. It was better in the second half, but when you play every three days it is difficult to know what is psychological and what's physical.
"There's a psychological part of it, for sure, because we didn't really go for it at the start again."
Rafael Benitez was delighted with a third home victory as interim manager, which keeps Chelsea only six points behind City in second place.
"We had a lot of chances in the first half when we were on top of them, controlling the game," he said. "Even in the second half we had situations on the counter-attack where we could have scored another. I am really pleased. The players put in a great effort and it was a great game."
Benitez confirmed that Ashley Cole plans to sign a new one-year contract at the club. (© Independent News Service)