The Reds took a giant step towards avoiding the drop with a 1-0 home win over Coventry at the weekend.
Another Victory at Bloomfield Road in the division's early kick-off would move Forest six point clear of third-bottom Norwich, who have just two matches remaining, and pile the pressure on the other sides who are not yet safe from the drop.
"I was always quietly confident that we would get out of trouble, that we would stay up," said Davies. "It is in our own hands now and it could all be over on Saturday.
"The result against Coventry puts us in that position - it was a huge win for us. If we win again, when you look at the other fixtures, results could go our way and we could be safe.
"At this moment there are six or seven clubs who can get dragged into it. I think you will see one or two surprises in terms of the teams who find themselves looking over their shoulders."
The Reds climbed out of the relegation zone with a hard-fought 1-0 home victory over Coventry on Saturday at the end of a week that had begun with a battling goalless draw at Sheffield United, where they had played for 75 minutes with 10 men.
Forest are unbeaten in four matches having previously come from behind to draw at Barnsley and edge a thrilling 3-2 win over Bristol City at the City Ground.
Davies said: "The players are learning in terms of how to defend leads and hold onto wins, and that is the pleasing aspect. It is a great answer again to the question of whether this team can play under pressure.
"With the injuries we have had and the suspensions we have had, we have had to chop and change the side and it has not helped. So with all of that, we have to be very pleased. It has been a fantastic effort."