"Gretna are dangerous opponents for two reasons," observed the Kilmarnock boss. "One, you don't want to be the first team they beat and two, they will be trying harder than ever to get that first win.
"It doesn't matter who's playing them. If we beat them on Saturday, it then goes on to the team who plays them the following week. It will end sometime and from a Kilmarnock point of view we have to make sure it doesn't happen on Saturday."
There will be no complacency within the Killie ranks suffering from a growing injury list, as Killie try to get back on track following narrow back-to-back league defeats against Rangers and Aberdeen.
"It's another tough away game for us," added Jefferies.
"The players will be well warned not to take them lightly or look at their results. The results are a bit false and they have deserved a point or two more.
"They worked hard to get here and they will be the underdogs in every game. But Gretna are a very unlucky side to be sitting on one point given their start to the season."