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."
Preston boss Simon Grayson was staying positive after losing only his second game in nine since taking over at Deepdale.
He said: "With the amount of possession and chances we have had we have done enough to win the game. In this game and our previous two games we have had more chances to win games than some clubs will get all season.
"You would be more concerned if we weren't creating the chances but we are just not ruthless enough or quick enough to react in the 18-yard box. You can't fault the players for their work and commitment it's just not taking clear-cut chances but when we do someone is going to be on the end of a right tanking."