Bayern Munich's missed chances at Augsburg left coach Niko Kovac and star winger Serge Gnabry frustrated as the Bundesliga champions had to settle for a point.
Kovac's side recovered from Marco Richter's first-minute opener and then led when Gnabry teed up Robert Lewandowski before scoring himself.
However, Bayern passed up two big opportunities to stretch their lead, with Augsburg goalkeeper Tomas Koubek excelling while Thomas Muller, who has made his frustration at a lack of match action clear, was guilty of a glaring miss.
This profligacy came back to bite Bayern as Alfred Finnbogason struck in second-half stoppage-time, pouncing on an error from Lucas Hernandez - another man in the spotlight following a fitness row with France.
Both the slow start and the failure to put the game to bed were of great annoyance to Kovac as he faced the media at full-time, with his side third ahead of leaders Borussia Monchengladbach's clash with Borussia Dortmund.
"We started very badly in the game. That must not happen to us, as we have previously pointed out," he said. "We have to be awake [immediately] and not be there in five minutes.
"But then we had everything under control. We had the ball and huge chances but did not score them. If you cannot do that, you cannot concede a second goal at the back.
"Two shots on goal, two goals [for Augsburg]. That annoys me."
Gnabry took a similar tact, adding: "We have moved on from the last game against Hoffenheim [a 2-1 defeat before the international break]. We came out fresh and played a great game, controlling it all the time.
"We ended up with two almost 100 per cent chances to get a third. If we score, the game is over. That's where we spoiled it.
"We had a lot of possession and a lot of chances - we should have won, but we were a bit too careless and then something happened at the back. That's football."