Arsenal FC are on the verge of exiting the Champions League after crashing to a record 5-1 defeat at FC Bayern Munich on Wednesday as Thomas Mueller netted twice.

Robert Lewandowski, David Alaba and Arjen Robben were also on target as Pep Guardiola’s FC Bayern Munich emphatically avenged their 2-0 defeat at the Emirates Stadium a fortnight ago, their only loss of the season.

“That was a key game for us, otherwise we would have had a lot of work to do in the group,” Mueller told ZDF.

“If we win our next game now, we should be through, so tonight was a big step.”

France striker Olivier Giroud scored Arsenal FC’s consolation goal with 20 minutes left while, between them, Mueller and Lewandowski have scored 31 goals for FC Bayern Munich in all competitions this season.

This was Arsenal FC’s joint heaviest away defeat in Europe, equalling the 4-0 drubbing at AC Milan in the last 16 in February 2012.

“The early goal freed FC Bayern Munich up a lot and on this occasion we had less courage than the home game,” admitted Arsenal FC’s Germany centre-back Per Mertesacker.

With two games left, Arsene Wenger’s side have only a mathematical chance of reaching the knock-out phase after Dinamo Zagreb’s 2-1 defeat at Olympiakos.

The Gunners have three points along with Dinamo, while Olympiakos and FC Bayern Munich both have nine with the Germans top of Group F on goal difference.

“We have to win both games and get two goals on Olympiakos, but it’s not over and thata s how we have to approach it,” added Mertesacker.

Arsenal FC next host Dinamo in a fortnight, then play Olympiakos away in their final game.

“We need to bounce back and put away negative energy,” said the Arsenal FC star.

Only seven of the Arsenal FC side who beat FC Bayern Munich at the Emirates Stadium started at the Allianz Arena on Wednesday.

Injury woes: Horrifying Arsenal even after Halloween

The Gunners have a horror injury list with nine of their squad out including the likes of Theo Walcott (calf injury), Alex Oxlade-Chamberlain (hamstring), Mikel Arteta (ankle), Aaron Ramsey (hamstring), Jack Wilshere (calf), Tomas Rosicky (knee) and Danny Welbeck (knee).

Guardiola had no such injury concerns and opted for fleet-footed wingers Douglas Costa and Kingsley Coman on the flanks with Netherlands captain Robben on the bench.

The hosts got the early lead when Thiago floated a cross over the Gunners’ defence and Lewandowski flicked his header into the Gunners’ net on 10 minutes.

The lead looked to have lasted just three minutes when Arsenal FC’s Mesut Ozil put the ball in the FC Bayern Munich net with his shoulder, but the Germany midfielder was booked for a handball and the goal was not given.

FC Bayern Munich doubled their lead with the half hour approaching when Coman fired in a shot, which was blocked, and Mueller stabbed home the rebound, which took a deflection off Mertesacker.

Arsenal FC goalkeeper Petr Cech palmed a Mueller shot over the bar, but FC Bayern Munich went into the break 3-0 up when left-back Alaba unleashed a fierce left-footed shot which flew past the Gunners shot-stopper.

Robben scored with his first touch, less than a minute after coming off the bench when he flicked Alaba’s pass into the Arsenal FC net for his first Champions League goal for more than a year on 55 minutes.

Giroud offered Arsenal FC brief hope by volleying home with 20 minutes left after making the most of an innocuous Alexis Sanchez cross for the Frenchman’s fifth goal in six games.

Mueller grabbed his second and FC Bayern Munich’s fifth on 89 minutes when he slid his shot under Cech to compound the Gunners’ misery.