Fly half Josh Lewis scored a try on his full Guinness PRO14 debut for the region while man-of-the-match Ollie Griffiths and Aaron Wainwright crossed the whitewash in the first half.
However, the South Africans hit back and scored four tries in all, as they battled back from 17 points down to force a dramatic second half as the Dragons eventually won 27-22.
“We just needed to win today to settle us down,” he said. “Last year we spent a lot of time talking about win or learn. Today we take the win and we learn too.
“It was frustrating that we didn’t kick on at 17-0. We didn’t put the foot down and accelerate on and take the game out of reach.
“We are still getting game time together and the back row haven’t played together and the half backs are a new pair so we got a bit loose.
“The yellow card (for Rhodri Williams), from a situation when we were exiting and didn’t get our kick chase right, saw them hurt us in that period.
“They got their gander up and because we haven’t played a lot together we got nervous and that played into their hands.
“Our physicality was exceptionally," he added. "You look at the bench we brought on and we made some big hits.
“We got a bit narrow and they are the team in the competition who will attack that space on the outside better than anyone else.
“There is lots to work on, but we take that win and we get started.”
Jackman also praised his new-look back row and the impact of Ross Moriarty on debut.
“Ross said he felt sluggish – so I am looking forward to seeing him when he is better,” he smiled.
“When we needed him he gave us that go forward and he has been brilliant off the field too.
“The Ospreys had a great win last week and their marquee signing was George North – he played a big role in that.
“Ross didn’t score today, but he has had that kind of influence for us.
“The boys feel better with him in the group because he doesn’t talk any nonsense and he is a man of action.
“That back row, with Wainwright, Griffiths and Ross plus the likes of Lewis Evans, Nic Cudd, James Thomas and Harrison Keddie, is our strongest sector. We need to make sure those boys play to the level they can.”
