If Leeds come unstuck against Headingley visitors Bath on Sunday, and Northampton beat Worcester, then Davies' men could find themselves cut 10 points adrift at the Premiership basement.
The Tykes have 11 league games left, and it is at home where they must start winning, especially given that four teams currently outside the Premiership's top-five - Bath, Bristol, Worcester and Saracens - have still to visit Headingley.
"We are in a difficult position, but we have got experience in that department unfortunately," said Davies.
"We are at the halfway stage and we have been in better shape, but in the last eight weeks we have shown a lot of resilience and character. It feels like a different side from a couple of months ago.
"If there was a corner to be turned, it has been turned. We have been picking up momentum, but the results against Newcastle and Gloucester (over Christmas) were disappointing.
"The defeat to Newcastle was particularly frustrating, given the amount of possession we enjoyed and the chances we created, especially in the first half.
"Our recent performances had certainly given us plenty of confidence, but we needed to show more patience in that first half to try to open up Newcastle.
"Last week's game against Gloucester was frustrating for other reasons. Kingsholm is a hard enough place to go to at the best of times, but when you are reduced to 13 men (Leeds had Rob Rawlinson and Gordon Ross sin-binned in the opening 20 minutes) you are left with a mountain to climb," he added.
"I thought the players showed real pride and determination to come back once the game returned to even sides.
"We can draw some positives from the fact that when the sides were even, we outscored them 7-3, but we are not kidding anyone - that does not get us any league points, and that is what we need."
Northampton, buoyed by a New Year's Day success against Bristol, still have numerous injury problems, but key performers Carlos Spencer, Bruce Reihana and Steve Thompson all start against a Worcester side who have lost their way in recent weeks, suffering defeats to Connacht (in the European Challenge Cup), Bath and latterly Newcastle.