The Scarlets still have a chance of qualifying for the Heineken Cup quarter-finals or the Amlin Challenge Cup if they can deliver a big win out in France against Perpignan on Sunday.
"We are still in the fight, we have a difficult place to go and get a result but there is so much at stake you don't need much more motivation," said Davies.
"For us, to still be in with an opportunity for the Heineken Cup next stages or Amlin on the last weekend is a significant step forward for this squad from where we have been and it shows the progress we've made in the last 18 months."
"I am very proud of the boys (for their performance against Leicester), they gave everything they had to give. Every one of our Scarlets players put that shirt on with pride and put their all into that game. They were committed and kept going until the end. The players will know as individuals and collectively that they gave Leicester a run for their money."
In injury new the Scarlets also confirmed that centre Regan King would be out for two to six weeks with a calf injury.
Hooker Ken Owens had an operation on his neck early last week and would be out for three to four months.
George North is progressing well with his rehab following shoulder surgery and Rhys Thomas (Tighthead Prop) is back training with the squad this week after recovering from a leg fracture.
Fellow Props Peter Edwards and Deacon Manu - both of whom picked up forearm fractures are expected to be out of plaster this week.