"The sooner we put it to bed the better," said Moriarty, whose team need just a point to be certain of avoiding a play-off with an Italian team.
Glasgow must win and hope Borders lose if they are to retain their slim hopes of Heineken Cup rugby next season.
The Warriors have lost their last six league games and are one from bottom.
"If we can get a win in Glasgow we can relax a little bit before Ulster come to Stradey," said Moriarty.
"It is difficult for everyone at the moment, the amount of games we are playing means there is a short turnaround and we can't sort things out in training, but we just have to get on with it.
"The performances are frustrating us because there is error after error in our game and we can't seem to get any composure."
The Scarlets will be without skipper Simon Easterby and fly-half Ceiron Thomas for the rest of the season.
Matthew Watkins and Mike Hercus face fitness races, while Dwayne Peel (ankle) and Barry Davies (groin) are unlikely to feature.