Tovey is suffering with a knee injury, while Hughes damaged his ankle in the game and they join Luke Charteris, Tom Willis, Ashley Smith, Ben Castle, Andrew Coombs and Scott Morgan on the sidelines.
The defeat, the Dragons' eighth of the season leaves them just one placed above bottom side Aironi in the RaboDirect PRO12 table. And Edwards has spoken of his frustration after seeing his side lose the opportunity to record their first victory in the competition since the end of September.
"You can't get away from that fact, the Scarlets gave away 19 penalties - maybe we had four clear ones (shots at goal) in front of the posts," he said. "The game's all about pressure, and we needed to get those points on the board.
"The Scarlets were able to make changes and bring in a fresh group of players and they responded extremely well. It's great for them in terms of their squad depth but not for us."
"We should have been able to put them away because on paper, on that field, we were the strongest team.
"Every game's important for us at the moment. We're going through a transition on the field and off the field," he said.
"We're trying to evolve into something where we are competitive every week.
"There's some good stuff coming into our game like our defence and we had a good first half (against the Scarlets) with our scrummaging, but other areas are letting us down.
"It's all about consistent parts together. It's our problem at the moment."