Corden found himself in hot water last year when he was accused of treating waiters badly at Balthazar restaurant in New York, with the owner claiming the star had been banned until he apologised.
But Brydon – who played Uncle Bryn in the hit comedy alongside Corden’s Smithy – said he thinks more should be made of what his co-star has achieved.
Speaking on the Rockwater In Conversation With podcast, he said: “James has a rollercoaster life and it’s very challenging.
“I don't think enough is made, frankly, about his success.
“Why am I not reading things that say 'Wow, look what he's achieved?' You never read that.”
Brydon said in his opinion it’s like it’s “a given” that Corden went to America to take over a talk show and that it then become “massive”.
He also said the TV star’s company has made a lot of other hugely successful shows.
“These things don’t just happen,” insisted the actor.
“I would like to see more of that rather than he sent an omelette back.”
After the restaurant scandal, Corden did address the issue on his CBS late night chat show.
He told viewers he had "made a sarcastic, rude comment about cooking (an omelette) myself”.
“And it is a comment I deeply regret,” added the star.
Watch: James Corden's The Late Late Show to be replaced by Game Show reboot