Daniel Sturridge scored the only goal at Villa Park as the Anfield outfit matched their one goal victory over Stoke to sit second only on goal difference to Chelsea at this early stage in the campaign.
"It was a terrific win for us," Rodgers told Sky Sports 1.
"The first half we had good control of the game and scored an excellent goal and in the second half we just needed to defend a bit more deeply today.
"If we open up too much they can really hurt you. Our aim was to just to keep our lines tight together and deny them many chances. It was a good win for us as this is a difficult team to play against.
"We looked calm on the ball in the first half some of our momentum was very good, our positioning was good, our mentality was good.
"In the second half you expect more pressure from them but overall Simon (Mignolet) has made a couple of terrific saves and we got three points."
Rodgers believes the strong start to the season, in contrast to last term when Liverpool only recorded their first league win at the end of September, is much to do with the mentality that has been developing at the club.
He said: "It's still very early. What was important was to make a good start.
"We didn't have a good start at all last year. Since the turn of the year we've been getting better and better.
"What's important now is the mentality of the group is to win and win together. We just have to keep it going."
Part of the improved belief can be put down to the arrival of defender Kolo Toure, who at 32 has helped to replace the experience lost following the retirement of Liverpool stalwart Jamie Carragher.
"He (Toure) has been brilliant," Rodgers said.
"Obviously you know Jamie Carragher well and it was very important to get someone in of a similar ilk.
"We need that experience. He's 32, he's fit and he's got that winning mentality and he's been very influential in the changing room."
Villa boss Paul Lambert was certain his team could take positives from the game.
While Villa might have not claimed any points, the Scot admitted he would have taken three points from the first three games of the season against Arsenal, Chelsea and Liverpool, if they had been offered.
"I knew it was going to be a big ask," Lambert said. "We have always been in the games. We just got beaten by one today.
"I can't be too critical of the lads because they have given everything. We're a young side but the improvement is there for everyone to see.
"If someone said, 'Would you take three points from these games?', I would have taken it with the start we had.
"The lads have been brilliant and we are going to keep doing what we are doing."