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The 22-year-old from Almora, a 2021 World Championships bronze medal, squandered a three-point advantage in the first game and a 7-0 lead in the second to surrender 20-22 14-21 to the two-time world champion Axelsen in a 54-minute semifinal clash.
Sen will have another chance to become the first Indian male shuttler to win an Olympic medal when he meets Lee Zii Jia of Malaysia in the bronze medal playoff.
India have never won a Olympic gold medal in badminton with PV Sindhu claiming a silver and bronze at the Rio and Tokyo Olympics and Saina Nehwal securing a bronze in London Games.