Nathan Dyer gave the visitors an early lead after five minutes, and a Wayne Routledge strike just after the break secured the three points for the Welsh team.
Rodgers was delighted with his side’s performance, and feels that the win could lead to more positive results away from The Liberty Stadium.
“For us it was important to go up a notch in terms of our resolve,” he told Sky Sports.
“Away from home we’ve had some terrific performances without quite getting the result but we said that going into the new year let’s make sure our resolve is that little bit more solid and then we will get points because we have quality.
“We’ve shown so far we’re going to be in with a chance to stay in this level and this great league and hopefully that continues.
“Our intensity, our pressure and our passing and quality when in possession of the ball I thought was magnificent – the players on the field and the supporters off it.
“The players have been magnificent. They have not been too hung up about not winning away because our performances have been very good and we started the year as we mean to go on.
“I feel confident that home and away we’ve got the game and the identity in the team to win. The players are just coming to terms with the level. Wayne Routledge – that was his first goal in the Barclays Premier League,” he concluded.
The win lifts Swansea up to 11th in the Premier League table, joining Villa on 23 points.
By Gareth McKnight