Adam Idah found the net on his Norwich return following a six-month injury lay-off, but the Canaries ultimately exited the Carabao Cup on penalties.
The Republic of Ireland striker thought he had marked his return with a late winner off the bench, only for Brooklyn Genesini to pull Bournemouth level in stoppage time and secure a 2-2 draw to take the tie to penalties.
Earlier, Emiliano Marcondes had cancelled out Jordan Hugill’s opener for the hosts as Angus Gunn shone in goal at Carrow Road.