The Crows trailed by 30 points midway through the second term but responded in the second half, piling on seven goals to the Hawks' three to snatch a three-point lead at the final change.
The visitors regained the lead early in the last quarter, but goals to emerging stars Patrick Dangerfield, Shaun McKernan, Taylor Walker and new skipper Nathan van Berlo ensured the club celebrated its 20-year anniversary with a win.
Adelaide struggled to move the ball with any purpose in the opening half, with most of the second quarter played in Hawthorn's attacking 50m.
Craig said his team's willingness to be more aggressive with the ball in hand in the second half had contributed to the comeback.
"I thought we were too easy to play against in the first half and there was a bit too much one-way traffic their way," Craig said.
"They were very slick when they got the ball even though I thought we defended reasonably well. We didn’t put that offensive pressure back on them and we spoke about that at half time.
"We made some slight changes on the night with our forward line and our ball movement, but in the end our persistence skill - and it is a skill - for such a young group…they need to remember that they've showed their cards now."
Debutant Brodie Smith showed promise after being subbed into the game in place of the injured Jason Porplyzia (shoulder) in the first quarter, while utility Shaun McKernan impressed in just his second AFL game.
McKernan finished with 15 disposals, eight marks and 13 hit-outs and Craig said he was pleased with the athletic big man's performance.
"Shaun was very good when you consider the importance of the game, on a big stage and against a quality opposition," he said.
"For a second-game player to perform like he did…he'll start to understand he can play at this level. He was good in the ruck, but I still think he can play a big role up forward.
"What you saw tonight was some flexibility, which is going to be important in the competition this year."
Opinion is divided as to how Adelaide will fare this season, following the retirements of club legends Andrew McLeod, Simon Goodwin, Tyson Edwards and Brett Burton.
Craig said the win over the fancied Hawks was proof his side could be a dangerous opponent this season.
"It was probably the youngest team that's ever represented this footy club out there tonight," he said.
"Our challenge is to continue that. There are going to be some ups and downs in the season, but I liked a lot of what I saw this evening."
