The Matildas were left devastated when Japan substitute Mana Iwabuchi swept home a late winner, ending their tournament in Canada.
Players lay strewn on the pitch for several minutes after the match, disconsolate at the 11th-hour defeat.
Stajcic said he was as gobsmacked as his team, which had held Japan at bay for all but four minutes of regulation time.
"I don't think there's much you can say after a game like that," he said.
"All you can do is put your hand around their shoulder."
It was a cruel end to the Matildas' campaign at the World Cup which, for the third straight time, ended in the last eight.
But taking the emotion out of the exit, Stajcic could already see the bright side.
Australia was a much younger side than Japan, which retained many players from its World Cup win in 2011.
Stajcic said this loss would enable his younger players to learn and grow ahead of next year's Olympics in Rio de Janeiro.
"Most of them are young players so it's a heartbreaking experience for all of us," he said.
"I'm proud of how we performed in a World Cup and I know there's so much growth.
"We don't want to compete with the best - we want to beat the best.
"By the time the Olympics come around, we want to take some more steps forward."
Stajcic, coaching at his first World Cup, said emulating Japan's technical prowess would significantly improve the Matildas.
"The Japanese girls have been together for five, six, 10 years - they've already won a World Cup, Asian Cup, silver medal at the Olympics," he said.
"Their chemistry's fantastic; their technique is superb.
"Our players, the bulk of our starting line-up are 20, 21, 22 (years old).
"We'll get there."
Matildas goalkeeper Lydia Williams said being sent home was devastating and heartbreaking.
"We had a great World Cup, made it out of the group of death, beat Brazil and really felt we were on a roll and about to create history again.
"To go out in the last few minutes of normal time was pretty devastating."
The result mirrors the Matildas' loss in last year's Asian Cup final and sends Japan into the last four, where it will play England for a place in the World Cup final.
Stajcic conceded Japan was a deserved winner.
"In terms of courage heart and spirit, (the Matildas were) fantastic. In terms of execution, not one of our best games," he said.
"Japan were the better team today. It was a scrappy way to score a goal but you can't say they didn't deserve their victory."
