The Welsh side went into the interval 6-3 behind at the RDS, but three breakaway tries from Brendan Macken, Ian Madigan and Fionn Carr saw the home side pull away.
That result left Edwards' men now propping up the RaboDirect Pro12 table, without a point from their opening two games ahead of Saturday's fixtures.
Edwards said: "This is a hurdle we've got to overcome here at the Dragons, we were in the game until half time and the start of the second half was crucial for us to put our marker down and to not let them do that to us.
"It was loose from our point of view and I'm very disappointed in the manner we conceded those tries.
"Whenever they came in to our half they took their chances and I thought they played as a team and did the basics very well and put pressure on us."
Despite the loss, Edwards did take some encouragement from the performance, particularly from last week's loss at home to Munster.
Jason Tovey scored a try, a penalty and a conversion for Newport but their hard-hitting defence was equally pleasing for Edwards, who challenged his side to convert those positives into points.
He added: "This team has taken great strides forward from our performance last week to tonight.
"We looked threatening in attack and there was some great defensive collisions but the hurdle now is to win these games on the road or at least challenge after half time."
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