The former Atletico Madrid shot-stopper returned to his hometown and made a number of key saves in the first leg of the UEFA Champions League Round of 16 tie at Estadio Santiago Bernabeu as United earned an important 1-1 draw.
The 22-year-old goalkeeper has received criticism for a lack of consistency since his 18.3 million pound move in 2011, but Bosnich says the "outstanding talent" on show on Wednesday night is De Gea’s real identity.
"That's just a matter of practice and timing," Bosnich told talkSPORT. "What he's actually got and what you are working with is something very special.
"You saw that last night, they were miracle saves that he was making. They are the saves that win you a game or get you through a tie like this. He proved everyone wrong against Real Madrid. 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 colors last night.”
Bosnich, who represented United 26 times during two spells, also praised Cristiano Ronaldo’s performance after the attacker netted Madrid's equalizer with a fantastic header after Danny Welbeck opened the scoring.
"When you watch it in slow motion, how high he got up, it was phenomenal," Bosnich said. "It was a phenomenal leap and he's a phenomenal player.
"Lots of people don't like him because of the way he struts his stuff but no-one can deny what a fantastic player he is. He showed his class last night and he's going to be they will have to watch very carefully at Old Trafford, coming back to where he made his name he'll be wanting to put on a really good show."