Rodgers was speaking following his side’s impressive performance away to Liverpool, in which they picked up their second point on their travels this season.
The point sees them move on to 13 points for the season, securely in the top half of the table, and Rodgers is delighted with the way his side have progressed.
Rodgers told reporters: “The first few games have been finding out about this league and the quality.
“We’ve grown into it but to come to a big club with top players fills me with great pride, I thought we were outstanding today.
“I thought today we took a big step forward. I felt coming into the game that we were better equipped, we’ve had ten games in the Premier League, and we’ve now got the confidence to compete at this level.”
Rodgers' side didn’t have it all their own way though. In the opening few minutes, Andy Carroll should have put his side ahead, hitting the crossbar from six yards out, and the former Chelsea coach conceded they did ride their luck at times.
He continued: “We got a bit of fortune early on but you need that little bit of luck when it’s required. To play how we’ve played and create the chances was fantastic.
“I said to them [the Swansea players] afterwards there’s not too many teams that will come to Anfield and get clapped off by their supporters.”
It wasn’t just the team performance which impressed the Swansea boss, who was also quick to praise individuals such as winger Wayne Routledge.
“It’s been unfortunate for Wayne,” he added. “I’ve had to play him in a couple of positions because of the form of our wingers but Scott got a hamstring injury and I just thought it was too big a risk to play him especially when I’ve got someone of Wayne’s quality.
“He was outstanding, a real threat and took up clever positions between the lines.”
Goalkeeper Michel Vorm, who made a string of superb saves, particularly from Glen Johnson late on, was also subject to praise from Rodgers.
“When he’s called upon he’s got great agility,” he said.
“That’s his second clean sheet after one he got here for Utrecht. Not many 'keepers come to Anfield and get a clean sheet.”