Klopp's men are forced to come from behind to secure all three points, but it is in vain as Bayern Munich secured their 23rd Bundesliga title
Julian Schieber had handed the hosts the intiative midway through the first half before Daniel Baier and Kevin Vogt netted to put Augsburg in front on the stroke of half time.
Schieber added his and Dortmund's second 10 minutes after the interval before Neven Subotic stabbed home for Jurgen Klopp's men only for Robert Lewandowksi to add a fourth late on.
Dortmund dominated proceedings early on, but took until the 10th minute to muster the first opportunity of the encounter as Subotic saw his effort blocked before Jonas Hofmann fired the rebound wide.
However, the hosts took the initiative midway through the first half as Schieber smashed his shot past Alex Manninger at the near post having been picked out by Moritz Leitner.
Dortmund looked to make their domination count as both Felipe Santana and Nuri Sahin tested Manninger, but couldn't find a way past the Austrian.
Augsburg drew level on the stroke of half time as Baier smashed a 30-yard volley past Mitchell Langerak following a corner.
And the visitors moved in front just a minute later as Langerak could only palm Tobias Werner's hit across goal into the path of Vogt to tap into an empty net.
Klopp's side began the second half brightly and weren't behind for long as Schieber netted his and Dortmund's second in the 52nd minute having been played in by substitute Robert Lewandowski.
Jan Moravek saw his tame effort cleared off the line by Santana after the Augsburg man had rounded Langerak and the visitors were made to pay for the miss as Subotic stabbed Mario Gotze's free kick under Manninger to put Dortmund back in front.
Lewandowski then saw his header wrongly chalked off for offside after the burly Pole was picked out by Sahin from a free kick in a dangerous position with 20 minutes remaining.
However, there was no denying Lewandowski in the second minute of injury time following some good work in the Augsburg 18-yard box as Dortmund secured the 4-2 win.