With Brazil and Turkey to come, both sides needed a win to have any realistic chance of making further progress in the tournament.
But Milutinovic said there were signs of encouragement for China in their first World Cup appearance.
"We played well but it wasn't enough," he said.
We have two more games to go - losing is part of football
"The difference was that Costa Rica scored two goals. There is no mystery about it.
"I would have liked to start with a different result but it was not to be."
But he added: "This is a World Cup. We have got two more games and it's football so no-one knows exactly what will happen.
"We have two more games to go - losing is part of football."
Milutinovic added that he would have no problem in lifting his players for the next match - against Brazil on Saturday.
"When you play against Brazil, it's a dream," he said.
"You don't need motivation to play Brazil although of course it will be difficult."
Captain Ma Mingyu said he was disappointed by the lapses in concentration and inconsistency that he felt were responsible for China's defeat.
"Bora told us we must be focused for 90 minutes, but we lapsed and gave up two goals," he said.
"Costa Rica played well throughout the game while we were inconsistent."