The 18-year-old has been named in the Socceroos' 30-man squad for looming World Cup qualifiers after just 12 A-League appearances.
"I was lost for words. I didn't know what to say," McGree told reporters on Thursday.
"I didn't really think it was true, to be honest."
McGree started the season merely trying to get some meaningful A-League minutes.
But last-placed Adelaide's woes have gifted the versatile midfielder opportunities.
"Coming into the season, I thought that I would get maybe some minutes here and there," he said.
"But due to some unfortunate circumstances of injuries and players leaving, I was thrown in at an earlier stage than I expected...(it) has helped me get where I am now."
McGree has made an instant impression, with deft skills, high work rate - and a touch of aggression.
"I just like to throw my body around, go in hard," he said.
"I will never come and intentionally start a fight but if it happens I will be in there," he said.
McGree now hopes to make the cut when Postecoglou trims seven players from the 30-man squad next week for World Cup qualifiers against Iraq and the United Arab Emirates.
"It will be a good experience, I will be able to learn from the coaching staff and from the players," he said.
"I think I will just take it all in my stride and grow from the experience and hopefully do well if I get the opportunity."