The 18-year-old replaced hat-trick hero Raheem Sterling after 70 minutes against Czech Republic on Friday to become the youngest player to represent the Three Lions in a competitive game.
And he contributed to the final goal in the 5-0 Euro 2020 qualifying win after his saved effort was turned into his own net by defender Tomas Kalas.
Maurizio Sarri has used the 18-year-old sparingly this season, giving him 19 appearances in all competitions, and believes he is not ready for regular first team football .
However, ex-Arsenal striker Wright, who represented his country 33 times during his career, cannot understand the stance and insists Bayern Munich's interest in Hudson-Odoi is proof he no longer needs holding back.
“I think when we watched him in the Under-17s when they won the World Cup, he was one of the outstanding players," he told ITV .
“I think that listening to Gareth Southgate about he’s ready and how impressive he’s been and he’s got no problem bringing him in, he looks like an international, I thought: ‘That’s a message, that’s a message back saying how is this guy not playing?’.
“A message back to Chelsea, a message back to the manager of Chelsea.
“You look at him and he’s ready to go. Bayern Munich are showing that he’s ready to go. Why isn’t he playing?”
Hudson-Odoi could now be involved when England face Montenegro on Monday as he continues to defy Sarri's lack of faith at club level.
But he is likely to return to Stamford Bridge and remain a sidelined figure, with Eden Hazard, Willian and Pedro firmly ahead of him in the pecking order.
Southgate accepts Hudson-Odoi's lack of minutes in the top flight but believes he is ready to play a regular role for England.
“I know a lot has been said about what’s the selection policy, is it on form or capability,” he explained.
“In the end, the players have to have the quality to play in this shirt.
“Ideally you’d have them all playing regularly and ideally they’d have a certain number of games for their clubs but I can’t wait for clubs to pick players 50 or 100 times.
“That’s not the landscape we’re operating in.”