Wing Dafydd Howells and scrum half Rhodri Williams both crossed for tries on their league debuts at either end of the Rodney Parade clash.
But composed Benetton Rugby produced a streetwise display to get ahead and force Dragons to settle for a losing bonus point on the opening weekend.
“We were a little bit undercooked and a little over anxious with the errors we made,” said Jackman.
“The boys were so passionate about trying to get off to a good start and getting a win to kick-start us. Sometimes you can want it too much and snatch at things.
“If you look at some of the errors we made, handling errors for example, it was totally uncharacteristic.
“We gave Benetton so many chances to get set piece and their set piece is very good.
“It is very frustrating but we have to make sure we are getting better week by week and we come in on Monday with a good attitude and fix it.
“There are a lot of new boys and the good thing now is you have experience. They know that these things happen in rugby, no matter how much you want to win. But we’ll fix it.
“We showed some fight and spirit at the end to get a try and try and give us the chance of stealing the game at the end.
“Apart from our courage at the end, it is not a game we will take a huge amount from. But we’ll learn from the errors and how we didn’t handle certain situations.
Dragons face Isuzu Southern Kings next Saturday at Rodney Parade and Jackman knows the importance of getting a first win on the board.
“A win would settle us down so we need to get a win,” he added.
“It you look at Benetton, they didn’t do a huge amount but they’ve got confidence of winning away from home and they looked composed. We looked very frantic at times.
“There is energy there, but we have to cut out errors. We are backing them up too.
“We kicked to the corner but lost the lineout, then lost the next lineout, then gave away a free kick, they scored three points and we kicked it dead from the restart.
“That’s four errors and that can’t happen. When Gav (Henson) kicked a penalty in the second half we didn’t deal with the kick-off and they got field position.
“They suffocated us by having territory and at the end we are trying to run out of our own half. But we’ll fix it.
“I just think if we get a win it will settle down and you will start to see the players we have and the talent we have. They will be able to express themselves without fear.
“I take responsibility that maybe we built this game up too much and didn’t deal with the pressure as well as we needed to.”
