The Dragons had led 5-3 at the interval at Rodney Parade following a late try from Steffan Jones but the Blues put the game to bed in the second-half with a try from Alex Cuthbert and 13-points from the boot of Rhys Patchell.
Edwards insists his side should have won the derby match and warned the Men of Gwent to expect a tough week on the training ground.
“I don’t think you can say there were any positives after that. We should have won he game and have to be hard on ourselves.
“It was at home, a local derby against the Blues. We have to focus on what went wrong and not kid ourselves with the things that went well.”
Edwards reckons the match swung in the Blues favour when Neil Hennessy awarded their seven-man pack a penalty from a Dragons’ five-metre scrum.
The capital city region went on to snatch a try down the end of the field and closed the game out.
But the Dragons head coach insists his side cannot afford to blame refereeing decision for the defeat and can only blame themselves.
“There was a huge swing in momentum when we had a scrum five-metres out with three re-sets and the penalty when against us,” said Edwards.
“The Blues went up the other end and scored a try, which won the game. It was a real sucker-punch try for us – in the period they were down to 14-men we conceded seven points.
“That was the time to start generating momentum but we lost our grip on the game.
“You can say this or that could have won the game but if we start on breakdown decisions and what ifs then we would be on a slippery slope.
“You have to get your basic processes right and deal with that comes your way. We didn’t do that.”
The Gwent outfit face Munster in Limerick on Saturday and Edwards insists there must be vast improvements.
“It’s a tough league and if we are to get anything from Munster then we need a massive improvement at the contact area and with our starter plays off the set piece,” added Edwards.