Dragons made a stunning start to the league encounter with early tries from Josh Lewis and Jared Rosser, but only went in 12-5 ahead with a strong wing to their backs.
Cardiff Blues battled back in the second half as tries from Kristian Dacey and Owen Lane – to add to his first half effort - wrapped up the points.
“We needed to convert pressure into points,” said Jackman. “There was a very strong wind in the first half and, even though we played some good rugby, we were probably not enough points ahead.
“Our game management and winning kicking battles for territory was going to be key. But we made some basic errors that gave them possession and platforms.
“They were good with the ball and so it was hard to get the ball back. Once the Blues got eight points ahead we had to chase the game.
“I’m proud of the boys and a really brave defensive effort, we just didn’t get dominance at the attacking breakdown and any change out of our lineout maul our scrum. We know what we need to fix.
“We are gutted by it, but the boys out there felt we weren’t a million miles away,” he added. “We’ll stick together and get better. We’ll turn effort and hunger into wins.
“The only way you can do that is by being better at the detail, and that is having areas of the game where you are dominant. We didn’t have enough.
“We’ve got good players now who want to do well for the Dragons. The dressing room is incredibly disappointed.
“They are passionate about this region and we have a young team that will grow up together. It’s frustrating because you always want instant success. But you don’t always get it.
“We’ve brought in talent that will make us better, but we were up against a very good side."
Jackman also looked ahead to the rest of the season and revealed some of the targets that remained a key focus.
“There are a few things we need to tick off this season – getting an away win and winning a Welsh derby. That was the first opportunity and we have five more,” he said.
“The first quarter was really good. We got a nice try off set piece play and got good momentum and quick ball. We looked dangerous.
“But it is an 80-minute game and the big learnings for us are the second half against the wind and not being able to win the territorial battle. We need to look at our game management and we need to fix it."