The Bavarians, runaway leaders in the Bundesliga and favourites to lift the German Cup, played arguably their worst game of the season in front of a home crowd and toyed with elimination as the Gunners unsuccessfully tried to overtun the 3-1 deficit from the first leg in London.
"We have been playing disastrous football in the last three weeks," Hoeness told reporters. "If the team draws the right conclusions from this game then it is still five minutes to 12. But we will not be able to win anything in the Champions League playing like that."
"If we keep on playing like we did against Arsenal then we will not beat anyone."
At first glance Hoeness' anger may look out of place for a team challenging for three trophies, having conceded just 10 goals in 25 Bundesliga games and having carved out a huge 20-point lead at the top with only one league defeat.
But a closer look at their Champions League performance this season reveals they have been far less effective there.
As opposed to the Bundesliga, Bayern have kept only one clean sheet in the Champions League so far while also losing twice as many matches than in the league.
While the Champions League is obviously a tougher competition, the Bavarians have had a relatively easy ride in the group stage.
The faced teams such as BATE Borisov - to whom they lost - and Lille, neither a European heavyweight.
Wednesday's game was also the first of 37 matches in all competitions where Bayern failed to score.
"We must be glad to have made it through and now we need to be careful," said Hoeness. "For me this was a well-timed warning shot."
Bayern are desperate for titles after two seasons playing second fiddle behind champions Borussia Dortmund in Germany.
Last year's bitter Champions League final defeat against Chelsea has also left its scars, with the Bavarians eager to rectify it by reaching their third final in four seasons.
"It is very good that we suffered this setback in our otherwise sunshine world," said midfielder Thomas Muller. "This game raised a lot of questions in our safe, little world."
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