The Welsh region were knocking on the door as the clock ticked into the red - but Jones believes his side have only themselves to blame after failing to convert possession into points early on.
Two Jason Tovey penalties were all the Dragons had to show for their efforts in the first half and by the time Ross Wardle dotted down in the closing stages, Edinburgh had taken their own opportunities.
They will now will look to get back on track in Italy next weekend - and Jones has backed his side to reap the rewards of their hard work before long.
"The scoreboard was shaped by the first 25 minutes when we failed to take our points," Jones told the South West Argus.
"To score just six (through two Jason Tovey penalties) was not enough for the territory and pressure that we had that shaped the end of the game.
"We've got to take it on the chin and move forward. The boys have responded to a pumping against Connacht (24-8 two weeks ago) but the result wasn't to be and that's the reward that you want for working hard.
"There were lots of good individual performances but we were guilty of entering their 22 and kicking the ball away needlessly when we needed to be a little bit more positive."
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