Chelsea midfielder Ross Barkley was floating after his two-goal England performance for victory in Montenegro.
England struck five times after Montenegro had taken an early lead through Marko Vesovic. Michael Keane equalised before Barkley's brace gave the Three Lions a 3-1 lead.
Harry Kane and Raheem Sterling then added gloss but Southgate reserved praise for Hudson-Odoi.
Barkley said: "It was a great night for me. Montenegro was always going to be a hard test but we showed character to come back and put in a positive performance.
"From the first minute of the training sessions Callum Hudson-Odoi has been top drawer. He fully deserved the start."