The Gunners could only manage a 3-3 draw against Norwich on Saturday as they again dropped points at home.
However, Newcastle's defeat by Manchester City and Tottenham's 1-1 draw at Aston Villa means somehow Arsenal's Champions League destiny remains in their own hands.
Victory at West Brom next Sunday would seal third place, and with it automatic qualification to next season's group stages, which could well have already been secured but for another shambolic display at the back against Norwich.
After taking the lead inside two minutes through Yossi Benayoun, a blunder by keeper Wojciech Szczesny allowed the Canaries to level before the visitors led at the break through a deflected effort from Grant Holt.
Although captain Robin van Persie's second-half double put the Gunners back in command, their defensive frailties were exposed again when, with five minutes left, Norwich substitute Steve Morison broke clear to level things up.
It was the 47th Premier League goal Arsenal have conceded this season, and Wenger knows that is a statistic which must be rectified.
"Defensively what we did was not good enough. We lost too many challenges and were not committed," said the Arsenal boss.
"There is no obviously explanation other than Norwich played well and we were poor."
Arsenal created enough chances to have comfortably put the game beyond Norwich in the second half - although by then had decisions gone the visitors way, the match could have all been over as a contest, with referee Anthony Taylor failing to award the Canaries two penalties and on another day could well have shown Benayoun a red card for kicking out at Russell Martin.
The officials did not have the best of afternoons, as during stoppage-time Norwich defender Kyle Naughton clearly pushed Van Persie in the back just as he looked to tap in at the far post.
Wenger, though, admitted his side had also not been sharp enough in front of goal.
"We missed at least six chances in the second half, which at this level makes it difficult," said the Arsenal manager.
"The only chance we have is to win the last game and let us hope that we do not pay a heavy price for the fact that we could not win here. If you play against Norwich at home you have to win."
Gunners defender Coquelin called for focus on delivering the required performance at The Hawthorns, which will be Roy Hodgson's last game in charge before he takes charge of England.
"When you come back to 3-2 at home you expect to hold the result, and it didn't happen so obviously the whole team is really disappointed," Coquelin told Arsenal Player.
"We played better in the second half and scored two goals, but fair play to Norwich, they didn't give up and got the equaliser. We're battling for third, but this was a massive blow.
"It is not down to us now, we just need to focus on West Brom and try to claim the three points. We will give 100% until the end of the season.
"We have one last game and we need to win."
Arsenal suffered an injury setback when defender Bacary Sagna suffered a broken leg during the first half, which rules him out of France's European Championship campaign.
The right-back had recovered from a similar injury earlier in the season at Tottenham in October.
Sagna told French newspaper L'Equipe the incident happened in a coming together with Norwich midfielder Bradley Johnson, whom he claims purposely "stepped on my leg".
The 28-year-old, however, vowed to return stronger.
"That is how football is. It has happened to others before me," he said.
"I came back once, I will come back a second time, even stronger."