Dragons secured a first league win of the season when they defeated Isuzu Southern Kings 27-22 at Rodney Parade on Saturday.
Jackman admits his squad will need to raise their game again to match Leinster – who will also be eager to return to winning ways after a narrow away loss at Scarlets.
However, he insists the Dragons will have nothing to lose when they arrive at the RDS Arena in Dublin.
“We haven’t got anything to lose there,” he said. “We haven’t won away from home for a long time and we want to get that off our back this season. But there is no pressure on us.
“We can go and pick a couple of elements of the game that we really want to improve.
“The defence of the lineout maul will be one, we also need to get our kick chase right and defend space better. If we sort those three areas we will one step further ahead of Zebre.”
Jackman is also set to resist any temptation to make changes and instead give his team more time to gel in the first block of six Guinness PRO14 games.
“We erred on the side of caution in pre-season to get people fit,” he added. “We didn’t go hard in pre-season so we could have our key players together for the start.
“It makes sense to keep that group together and a settled team for this block of games and build that understanding that settled teams have.
“Not too many teams have brought in 14 new players and changed their coaching staff. We know it is going to take a bit of time, but we want to pick up points while we are gelling as a squad.”
