The Gunners boss saw his side capitulate for the second time in succession against the German champions.
Another 5-1 defeat saw Arsenal crash out of the Champions League at the last-16 stage again in spectacular fashion.
Their 10-2 loss on aggregate highlighted the gulf in class between the two teams.
Even star man Alexis Sanchez couldn't help claw back some pride for Arsenal, despite returning to the starting line-up at the Emirates.
Arsene Wenger feels Arsenal cannot match Bayern Munich in the transfer market
We can compete with Bayern Munich and we have shown that tonight in the first half
Arsene Wenger bemoaned the officiating as pivotal to the result as centre-half and captain Laurent Koscielny was sent off after conceding a penalty early in the second half when Arsenal led 1-0.
The Frenchman remained positive about his side's performance, but admits it is Bayern's ability to attract top signings where they differ from the north London outfit.
"I think we can compete with Bayern Munich and we have shown that tonight in the first half," Wenger said.
"I believe the second half was a very difficult situation for us.
Arsene Wenger could lose Alexis Sanchez in the transfer market at Arsenal this summer
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Arsenal player ratings against Bayern Munich
Tue, March 7, 2017
Express Sport brings you Arsenal's player ratings from their embarrassing 5-1 (10-2 agg) defeat to Bayern Munich
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GK: David Ospina – 0
Some Arsenal fans protested against Arsene Wenger's new contract on offer in the game against Bayern
"Bayern are a good team and they do what they want in Germany, which we cannot do in England.
"Nobody can compete with them, they take the players they want and they are a bit lonely on the market. That’s not the case in England."
Arsenal are set to go in search of a top forward this summer, as a replacement is set to be needed for Sanchez who is expected to quit the Emirates.
Lyon's Alexandre Lacazette and Borussia Dortmund's Marco Reus are on Arsenal's radar, but Bayern's array of stars still makes them far superior.