Goals from Jamie Mackie (18th minute) and Darius Henderson (in injury-time) sent Forest through to the final 16 as they beat the Lilywhites 2-0 at Deepdale in the fourth round replay.
Preston boss Simon Grayson felt his side were extremely unlucky in losing the tie and Forest manager Davies agreed.
"I think the best team lost," he said.
"On the night we didn't show enough quality, we didn't compete as well as the home team and you've got to feel sorry for them because they deserved to win the match. End of.
"It was a typical cup tie night of football, the rain was pouring down, the wind was blowing, the pitch was soggy and they handled it better.
"Their attitude was excellent, their energy was good and the best team lost."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball