The Alex announced the sad news on Friday that Dugdale and his partner Nicola had lost their baby, with the influential centre-back playing no part in today's 2-0 victory over Southend.
But his team-mates paid their own special post-match tribute by wearing t-shirts which read 'Duggy and Nicola - you're in our thoughts'.
Speaking afterwards, Crewe boss Davis said: "Adam lost his young son several days after he was born to a million, million, million to one chance, it was growth he got on his head. He lost his fight several days ago.
"He's not been in to the club for a couple of weeks now. I spoke to him yesterday morning about it, him and Nicola are holding up as best as they can.
"I told him the players were behind him, we tried to do something today for them. We got some t-shirts made and I'm sure the players put that little bit extra in for him.
"We're a family, we are that sort of club, and when something like that happens we rally and get behind people and that result was for him."
Wembley rose for a minute's applause in the sixth minute, Dugdale's shirt number, and it came just seconds after Crewe had taken the lead courtesy of a well-worked corner routine.
Davis admitted afterwards that his side had enjoyed little success practising the set-piece on the training ground yesterday, but it looked far from the case as Byron Moore's flag-kick was dummied by Harry Davis, son of Steve, and superbly swept home from 20 yards by captain Luke Murphy.
It was the start of an impressive display from the highly-rated 23-year-old, who dispossessed Bilel Mohsni four minutes after half-time to set up Crewe's second which was eventually converted by Max Clayton from close range.
Crewe lost highly-rated pair Nick Powell and Ashley Westwood to Manchester United and Aston Villa respectively after last season's npower League Two play-off final victory, and Davis is also resigned to losing Murphy after a second Wembley success in as many seasons.
"We haven't had any enquiries for Luke, a lot of people have been watching, maybe something might happen in the summer, who knows?," he said.
"He's a very talented lad, we feel he's better than Ashley Westwood because he's a goalscoring midfielder.
"Where he's going to go, I don't know, when he's going to go, I don't know either. I've had no enquiries but I'm sure something will come of that, maybe in the summer. And he'll go with our blessing because he's ready to go. We can't hold on to him forever."