Although the result suggests it was a walk in the park for the defending champions against a side who remain rooted to the foot of the Bundesliga table, Klopp says it was anything but easy.
"Augsburg played another really good game," he said.
"It was really hard work for us, but we expected that.
"It was a very tight game with some beautiful goals as well as some chances for Augsburg, which (goalkeeper Roman) Weidenfeller did really well to stop.
"When they made it 3-1, they were right back in the game again, but we still deserved our win."
Augsburg coach Markus Weinzierl accepted the latest round of compliments, claiming that his side could not really have done more than they did.
"I saw an engaged and courageous performance from my team," he said.
"We were tactically good, dangerous in attack and created several opportunities, only we are not rewarding ourselves for our efforts.
"We get nothing for the fact we were better or at least on a par with them in the first 45 minutes."