The Forest manager saw his side collect a sixth win on the bounce, cementing their place in the play-off places as a result.
Lewis McGugan was the hero as he came off the bench to net the winner with five minutes remaining after Darius Henderson had cancelled out George Boyd's opener for Hull. The visitors clung on thanks to some heroic last-ditch defending in the closing stages.
McGugan coolly slotted home from eight yards after Danny Collins' long ball had been headed down by replacement Dexter Blackstock and drilled across the area by another substitute in Billy Sharp.
"Sometimes it works for you and sometimes it doesn't," said Davies, whose side will match their club record of seven straight league victories, set back in 1922, if they can overcome Huddersfield after the international break.
"That's the type of impact we need from subs. We certainly went out and tried to win the game."
Tigers boss Steve Bruce felt his side were good value for at least a point after creating a flurry of chances late on.
"We've done enough to win two matches, that's the biggest disappointment," Bruce said.
"I couldn't fault the way we played or the way we've gone about it.
"To be fair to Forest they've gone for it and played three up front, but the attempts we've had off the line and the post - it's just one of those horrible ones where the luck goes against you. Unfortunately it wasn't our day."