Bradden Inman's first-half strike leaves Alex 10 points off the top six with just six games of the season remaining.
Crewe, who have lost only one of their last six matches, head to London on Sunday for the Johnstone's Paint Trophy final against Southend and Davis is hoping his side can make a return trip to the capital in May.
Davis said: "It was a boost for the squad to win the game before the final.
"It was also nice to get a home win with a very young team out. I think the average age was about 21 and to see them battle hard to get the win against a good Preston side was very pleasing.
"Bradden is a good finisher and he gets into good positions. When he gets into those positions everyone thinks he is going to score. We've missed him and having him back is a big boost for Wembley.
"I have seen some great performances and go away in a positive frame of mind before I pick the squad on Wednesday.
"But it's not just about Wembley. I want us to remain competitive until the very end because mathematically we are still in with a shout of the play-offs.
"As long as it is possible we can sneak into that top six then we will keep going and keep the season alive."