The 38-year-old was also pleased with contract negotiations and hints he could sign a new deal with the club in the near future
Swansea's slick performance at the Liberty Stadium earned them a 3-2 victory against Arsene Wenger's side, which lifted them into 10th in the Premier League.
Rodgers, who is set to be offered a new deal with the club, also revealed his players remained level headed after Sunday's win.
"It was a brilliant result for us and performance, and three great points that we really appreciated," he told reporters.
"But the players weren't jumping about all over the changing room because they had beaten Arsenal. They were relaxed and ready for the next challenge.
"It was nice for the players to get the recognition [in the media]. They have been absolutely outstanding this season.
"I know I have got a number of players who could play at that [international] level. Whether they get chosen or not is another factor.
"They play a game here that suits international level, so I would have no hesitation about any of these players who are deemed possibilities being good enough to play at that level.
"We are looking to keep this great momentum going. You want to win after winning, and that is the aim and the focus."
Rodgers is hoping to replace his one-year rolling contract with Swansea and expects it to be squared away before the month ends.
The 38-year-old was also buoyed after a meeting with the club's chairman, Huw Jenkins, and is excited to build on the progression of his side.
"It should be fairly straightforward," he said. "The basis of the contract is there, and hopefully we can put pen to paper very soon."
"There are obviously items I need to ensure around the contract, and likewise the football club, but I don't foresee any difficulty and I am sure in the near future we can get the solution.
"When I came here, I said I would do a one-year rolling contract, for people to judge me and see how I perform, and then we will go from there.
"The most important item in all of this is to make sure that both myself and the club keep moving forward. What I want to do is show my commitment in trying to build for the future.
"I have a brilliant relationship with the chairman. We both respect our jobs and speak very openly. He knows how much I enjoy it here.
"We talked about an array of items, and I was really pleased when I left the meeting.
"It is something that if we can make that commitment both ways, and it suits, then we will hopefully get it resolved, hopefully before the end of the month."