Zebre are without a win in their two Guinness PRO12 encounters so far this season, but having lost there twice in the past three years, Danny Wilson's men will be desperate for a win in Parma.
And 28-year-old back-rower Turnbull insists his side's progress will count for nothing if they come unstuck again against the Italians.
"The start of the season will probably mean nothing unless we back it up this weekend against a Zebre team that we haven't beaten there in a few games," he said.
"We've come a little bit unstuck a few times out there, so we'll have to go out there and get the win to put us in a better place again.
"Zebre can throw the ball about, and at home they've got such a strong pack as well and that's something we're going to have to deal with as a pack of forwards this weekend.
"We need to make sure we do our extras and make sure we know what to expect on the weekend. All credit to the boys, the team and the coaching staff as well so far."