The Blues, who are ninth in the RaboDirect PRO12, emerged with a 29-20 victory as Wales internationals Leigh Halfpenny, Alex Cuthbert and Rhys Patchell shared the points.
But Davies is aware that the Warriors are wounded animals and has urged his side to up their work rate further as they look to challenge Toulon for top spot in Pool 2.
"We were pleased with the motivation and spirit we showed last week," said Davies.
"We have been getting better all year and at the moment the performance levels are growing.
"We will need to work even harder up in Scotland. We need to go up a level physically and tactically, be more accurate with the ball.
"Last week was about desire and performance, this week we need to extract even more from the players.
"I expect Glasgow to play like men possessed. We looked to play a certain way last week against them and executed it.
"But we know how good they can be and have had some terrific games up there. Friday will be no different.
"The team that controls the ball in the opposition attacking third will be hard to beat.
"It's a tough game because they will have been disappointed by last week, but we need to build on what we have achieved in this competition."
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