The defeat, courtesy of another goal double from the Magpies' in-form Senegal striker Papiss Cisse, was Swansea's third in a row after reverses against Everton and Tottenham. It means Swansea are now on their worst run of league form since the early days of Kenny Jackett's reign in 2004.
With a comfortable cushion over the drop zone, Swansea should retain their top-flight status for at least another season, but Rodgers said: "We need to pick up some points and finish the season how it has been for us, this season was a real test of our talent, and we have passed that, it was also a test of our courage and mentality and we have passed that too."
He added: "What we have to do is finish the season off and make sure it does not drift off or fizzle out. We have to continue to fight, we will always learn at this level that if you are a fraction out of position or misplace a pass you get punished.
"Until our safety is assured we will not think about it.
"Our performance against Newcastle was very good but not the result, and we now have a run of games that are against sides fighting for their lives, but we are fighting for every point too."
Rodgers also defended the decision to leave leading scorers Danny Graham and Scott Sinclair out of his starting line-up, even though the pair have scored 17 of Swansea's 35 league goals, in favour of Luke Moore and Nathan Dyer.
Rodgers had admitted he planned to rotate his squad over the Easter period, and says he would not have done anything differently.
"I felt a lot of goals had come from midfield and we needed a bit of freshness up front," he said. "To stay at this level we needed 25 players not 12 or 13.
"Scott and Danny had not had many chances in recent games and I felt that Luke, he likes to come and join in and I thought he did that well but we could not find the pass or the goal to open up the game."
Source: PA
Source: PA