Turner's men conceded four tries against an on-song Blues outfit who made it maximum points from two home fixtures so far this term.
The Dragons recovered from a heavy defeat on the opening weekend away at Connacht to beat Glasgow Warriors at Rodney Parade a week later but their latest loss leaves them in 10th position in the Magners League table ahead of another Welsh derby against the Scarlets on Friday evening.
"It was a long 80 minutes. We knew it was going to be a real tough one, it's always a tough place to come, given the strength of the Blues squad and especially when we have got a whole back division out," said Turner.
"The basics of the game we didn't adhere to, there were far too many errors and we coughed up too much ball - we got what we deserved.
"They deserved their win against us. We never stopped battling but, at times, we were like rabbits caught in the headlights.
"We weren't smart enough and made too many errors. I felt we could climb back, and had the Will Harries try come earlier we could have made a game of it, but we made those errors.
"When the Blues bring on guys like Michael Paterson and Dan Parks is on the side, you're going to be under the cosh and they showed what a good squad they've got; 40-20 was about fair on the night."
The Dragons finished two places above the Scarlets last season, claiming the last automatic qualification spot into the Heineken Cup in the process, but the Men of Gwent have to look back three seasons to find their last league victory over the West Wales region.
With the injury crisis in Newport showing no signs of recovery, Turner has looked to the performance of the Blues for inspiration ahead of Friday night's clash.
"We need to build momentum and get phases into our game for next week, much like the Blues did against us.
"You couldn't fault our work ethic and mental toughness out there, which I had questioned during the week, it was just the basics."