Heidar Helguson's ninth goal of the season put the Bluebirds ahead before Darius Henderson was sent off for elbowing the veteran striker, and substitute Rudy Gestede sealed the win with his second-half brace.
Henderson missed Forest's best opportunity when he failed to convert from close range, while Lewis McGugan had an effort ruled out for a foul on Aron Gunnarsson as they dropped out of the play-off places and saw their 10-match unbeaten run ended.
"The run had to come to an end at some point," Davies said. "We have four games left and we know we need at least two wins. There will be plenty of movement in the coming weeks but it's the table at the end of the season that matters. It's all to play for."
Davies also confirmed Greg Halford had suffered cuts to his head and dizziness after being carried off when he took a blow to the head from Rudy Gestede's knee early in the second half.
He will be assessed ahead of Tuesday's meeting with Middlesbrough.
- Sports & Recreation
- Rudy Gestede
- Darius Henderson