The Dragons, who currently sit ninth in the GUINNESS PRO12 table, had started brightly and scored tries from Matthew Pewtner, Taulupe Faletau and Ashley Smith.
But second-half mistakes proved costly as the Dragons missed ten points from the tee, wasted three attacking five-metre lineouts and gifted the Falcons two tries after Hallam Amos' kicks were charged down.
And former Wales international Jones admits that the performance was not good enough from his side.
"I'm a bit numb. Individual errors, some of which were Keystone Cops standard, gifted Newcastle 17 points," he told the South Wales Argus.
"Losing three five-metre lineouts was hugely disappointing, we should have scored at least one of them. The way that we went about calling them and deciding what we were going to do was just not good enough.
"The game is about scoring points and not conceding, when you are scoring 26 you'd expect to win at home.
"I've got to give Newcastle credit, they were organised, fought hard and worked for the jersey but it's not the result we were hoping and looking for.
"We are a group that are trying to grow and we need those victories to help that growth. We've got to take it on the chin and move forward."
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