The former United keeper believes the 22-year-old can now be a fixture in the Old Trafford goal for years to come.
"David De Gea proved everyone wrong against Real Madrid," Bosnich told talkSPORT. "He is an outstanding young talent.
"He's come to England at a young age and has had to adapt to the culture of high balls during games. It's taken him a little bit of time to get used to it but he showed his true colours last night."