"We gave away possession, dealt with crosses badly. This is a bitter setback for us and our confidence."
The Bundesliga leaders suffered only their second league defeat this season and their third in all competitions while Augsburg escaped the bottom three.
Second-placed Borussia Dortmund can now trim Bayern's four-point lead when they host Stuttgart on Saturday.
Thick fog shrouded the Augsburg Arena, but the hosts were crystal clear with their game plan.
Brazilian left-back Iago caused havoc on the flank as Augsburg, who were third from bottom before kick-off, raced into a deserved 2-0 lead.
Iago floated in a cross to Swiss striker Andi Zeqiri, who laid the ball off to Pedersen to drill his first Bundesliga goal past Manuel Neuer after 23 minutes.
With Kimmich again watching at home having only been released from house quarantine on Tuesday, Bayern struggle in midfield.
Augsburg doubled their lead to the joy of home fans when Kimmich's replacement Marcel Sabitzer lost possession and Iago again swung in a cross which Hahn headed home on 36 minutes.
Bayern responded when Thomas Mueller deftly flicked the ball into the path of Lewandowski who drilled his shot home despite Augsburg goalkeeper Rafal Gikiewicz getting a glove to the ball.
With Bayern 2-1 down at the break, Julian Nagelsmann plugged the pace on the flanks by bringing on right-back Alphonso Davies - who Mueller nicknamed 'Bayern's Road Runner'.
The fleet-footed Canadian stemmed Augsburg's attacks on the flank and had two clear chances, but with twenty minutes to go Nagelsmann added a second striker with Eric Maxim Choupo-Moting alongside Lewandowski.
With time ticking down, Lewandowski was denied by a great save from Gikiewicz as Augsburg held on for the first win over Bayern since 2015.