But at the other end of the age spectrum, 17-year-old Charley Hull did receive one of Neumann's four captain's picks as the Swede finalised her team to defend the trophy at Colorado Golf Club in Denver from August 16-18.
England's Jodi Ewart Shadoff, Sweden's Caroline Hedwall and Italy's Giulia Sergas received the other wild cards, with Davies having already let the cat out of the bag after missing the halfway cut in the Ricoh British Women's Open at St Andrews.
"Oh well, no pick from the captain," Davies wrote on her Twitter account on Saturday. "Didn't really deserve one. Mind you still a bit disappointed."
Davies made her Solheim Cup debut in the inaugural competition at Lake Nona in 1990. Over the next 21 years she became a stalwart of the European side, appearing in all 12 events.
In her last appearance, at Ireland's Killeen Castle in 2011, she became the highest points scorer in the competition's history, her total of 25 passing Annika Sorenstam's old record of 24.
"It's always difficult when you come down to this and it's hard to talk to some of the players not on the team," Neumann told Sky Sports News. "On the other hand I am super excited about the four picks I made.
"I think she (Davies) is disappointed. Just looking at the way she has played she knew she was not going to be a pick, but she was very good when I spoke to her on the phone. She said I wish you all the best of luck, go out to Colorado and get it done."
Teenager Hull finished second in her first five tournaments this year and Neumann added: "I feel that she is playing fearless golf. You look at her stats and she shoots in the 60s about 30 per cent of the time which is pretty good.
"She finished runner-up five times this year on the European Tour, she is a strong player. I think she brings what we are looking for which is good energy and she is a long hitter which is good for Colorado.
"I think she can bring a lot of great things for the team so I am very excited about her being on the team."
Europe have never won the Solheim Cup on American soil, but Neumann added: "It is so difficult for us over there, the crowds are hard, but if this team can mentally prepare for this I really believe this team can do it."
American captain Meg Mallon had two wild cards and selected Michelle Wie and Gerina Piller.
European Solheim Cup team:
Suzann Pettersen (Nor), Carlota Ciganda (Spa), Catriona Matthew (Sco), Caroline Masson (Ger), Beatriz Recari (Spa), Anna Nordqvist (Swe), Karine Icher (Fra), Azahara Munoz (Spa), Charley Hull (Eng), Jodi Ewart Shadoff (Eng), Caroline Hedwall (Swe), Giulia Sergas (Ita).
United States team:
Stacy Lewis, Paula Creamer, Cristie Kerr, Angela Stanford, Brittany Lincicome, Lexi Thompson, Jessica Korda, Brittany Lang, Lizette Salas, Morgan Pressel, Michelle Wie, Gerina Piller.