Anne Keothavong's team were seeking to become only the fifth British side to contest the final in its 61-year history.
Raducanu gave the team the perfect start by beating Viktoria Hruncakova in straight sets but, following Boulter's 2-6 6-4 6-4 defeat, Heather Watson and Olivia Nicholls lost 6-2 6-2 to Hruncakova and Tereza Mihalikova.
"Right now it is difficult because I really thought we could do it as a team," said captain Keothavong.
"I have to maintain positivity for myself and team and find a way to pick everyone up. We're all absolutely gutted.
"I'm so proud of this team. We still reached the semi-finals and that’s a fantastic achievement."