The Reds struck early at Villa Park, with just 21 minutes on the clock when Daniel Sturridge produced a flash of brilliance to unlock the home defence.
Rodgers' side dropped deeper and deeper as the game went on, inviting pressure, but held out to secure back-to-back victories in the Premier League and successive clean sheets.
On the Reds' performance, Rodgers told Sky Sports: "It was a terrific win for us. I thought first half we had good control of the game and scored an excellent goal.
"Obviously second half, we just needed to defend a bit deeper today. Tactically that was the idea. In the first two games, Aston Villa have been brilliant on the counter-attack and if you open up too much the spaces, then they have players who can hurt you. We defended at half-pitch, kept our ends tied together and tried to deny them any chances.
"It was a great win for us because they will be a really difficult team to play against. It's big credit to Paul (Lambert) because he's set the team up very well and obviously it was a tough game for us."
Asked what had pleased him most, Rodgers added: "I thought we were calm on the ball in the first half. We were fluid in our game, there was good movement.
"We had half an idea on controlling it, the balance of the team when we have the ball, because if you open up too much against these, they can really hurt you with their pace on the counter-attack.
"I thought our positioning was good, mentality was good and tactically we fell back into our shape very well in the first half. Second half, of course you expect a bit more pressure from them. But, all in all, although Simon (Mignolet) had to make a couple of good saves, it was about the three points today and we got the three."
Liverpool have now taken maximum points from their opening two fixtures for the first time since 2008, but Rodgers will not be getting carried away.
He added: "It's still very early. What was important for us was to make a good start. We didn't have a good start at all last year, it took us until the end of September to get our first win, so I just think that since the turn of the year, since January, we have got better and better.
"We'll play better than we have done today at times, but what's important now is the mentality in the group is to win. We have shown a lot of really good signs and we just need to keep it going."