The Croatia players were given a standing ovation by their fans after taking the game to the French for the entire 90 minutes, dominating much of the match but falling to an own goal, a penalty awarded by VAR and two second-half strikes.
The 51-year-old gathered his players in a circle on the pitch and told them they should in no way consider the defeat a failure.
"Of course, we are downcast, but I told them 'hold your heads up high. You have no reason to feel dissatisfied, you have given your all and you have to be proud of your performances at this tournament'," he told a news conference.
"'Chin up lads, if somebody had offered us to be runners-up at the start of the tournament, that would have been fantastic'.
"'Sometimes in football you lose, that's football, but we were dignified in our victories and we must be dignified in defeat, we have to respect the scoreline,' that was the message to my players."
The Croatians had come back from a goal down in their previous three games, slogged their way through six periods of extra time and two penalty shootouts to get to the final - playing the equivalent of an entire match more than France.
They again came from behind on Sunday when Ivan Perisic fired home an angled shot in the first half but they were 4-1 down when Mario Mandzukic punished a mistake by goalkeeper Hugo Lloris in the 69th minute to make amends for his early own goal.
"But that in no way diminishes France's win. Maybe we were a bit unlucky, in the first six games we were favoured by luck.
GOOD FOR GAME
Dalic said he thought overall VAR was good for the game.
"Don't take this as me a saying something bad about the referee," he added.
"I respect the referee, he made the decision he thought was right. On VAR, when it goes in your favour it's good, when it goes against you it's bad."
"It was beautiful working with the lads (but) I never make decisions overnight," he said. "At this moment I'm not thinking about anything but getting safely home to Croatia."
Dalic said the success of a team representing a country of only four million people showed what could be done with a dream and lots of hard work.
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