The 67-year-old coach had warned his team they would be in for a tough afternoon but goals from Thomas Muller and Mario Gomez secured the three points
Despite sitting bottom of the Bundesliga table, Markus Weinzierl's side caused the league leaders plenty of problems during the 90 minutes, before a Thomas Muller penalty and a Mario Gomez effort clinched the win for Bayern.
“Before the match, I told my team very clearly it wouldn’t be a stroll," Heynckes told the club's official website.
"That was a hard job of work. As we all saw in the first-half, everything that’s been written and said is wide of the mark. FC Augsburg were made out to be less capable than they really are. Their organisation was extremely good in the first-half, their pressing was excellent, and we had a few problems getting going as an attacking force.
"We did better after taking the lead, and we had complete security again once we were 2-0 up. We showed the dominance and the authority which are our hallmarks.”
The result sees Augsburg remain in 17th spot and level bottom of the Bundesliga, but Weinzierl remained upbeat after the game.
“Congratulations to FC Bayern. Taking the full 90 minutes into account we have no complaints about the result, and it’s a deserved win. We gave a very, very good account of ourselves in the first-half," he added.
"We were extremely well set up to deal with our opponents, we didn’t look for a hiding place, and we didn’t want to pull everyone back. A goalless draw at half-time would have been deserved, but they were awarded the penalty, and goals like that really hurt you.
"We still came out for the second-half with high hopes and good intentions. Their second goal showed what individual class really means. That was the straw that broke the camel’s back, and you could see we no longer believed we could turn it round before the end.”