The Bundesliga outfit were narrowly edged out of Europe's second tier club competition in the Round of 32 second leg at Anfield in what was a solid display despite being hit with a number of injuries.
After the match, Klopp spoke highly of Markus Weinzierl's side who performed admirably both home and away against the Reds only to come up slightly short.
"It was a very tough game and they showed their determination to play and also made it difficult for us to play against them," said the German.
"They took risks and defended very well. If you look at it overall and the work Markus has done, he has got a great team and done really well – particularly given the injuries they've had.
"But it's less important what we think about them, I think it's important for FC Augsburg to feel very proud tonight."