Goals from Stefan Kiessling and Lars Bender helped Leverkusen end a run of four matches without a win in all competitions.
Augsburg had been unbeaten in the league this year before the loss, and Lewandowski hailed his side's improved display.
"The fact that Augsburg had not lost a single game since the resumption in fixtures in January was no coincidence," Lewandowski said.
"Against Mainz and against Schalke they were definitely the better team. Today, what was positive for us was that we played with full commitment at both ends of the pitch, and we had missed that recently.
"Related to that was our efficiency in front of goal, which was a lot better today too, and that's what decided the game in our favour.
"We played better football in our previous games, and we weren't able to achieve that same level of speed and precision.
"We worked hard for this today but we definitely didn't play as strongly as in our recent games.
"The important issue today was getting all three points and the fact that we addressed an issue which I have talked about in the past, namely delivering full commitment in defence and in attack."
The win, which came despite Sascha Moelders pulling a late goal back for Augsburg, kept Leverkusen a point behind second-placed Borussia Dortmund.
Lewandowski said the victory was more about returning to winning ways and three points than gaining confidence.
"Our confidence was definitely there before this game. In our previous matches in Gladbach or against (Borussia) Dortmund, but especially against Borussia Moenchengladbach, we had the feeling that we were actually playing really good football but were only missing a final ingredient," he said.
"I don't think this win was absolutely necessary for our confidence, but the points were important though."
