With the score level at 1-1, Argentine referee Nestor Pitana changed his initial decision and awarded a spot-kick, converted by Antoine Griezmann, for handball against Ivan Perisic after viewing television replays.
Dalic defended VAR (the video assistant referee system) as a "good thing for football" but believes his side's luck in Russia finally ran out after penalty shootout wins over Denmark and Russia on route to the final.
"It in no way diminishes France's win. We were a bit unlucky. Maybe in the first six games we were favoured by luck and today we weren't.
"I have to congratulate my players. Maybe today we played our best game at these championships. Against such a strong side as France you must not make mistakes. We are a bit sad but we must also be proud of what we've done."
Dalic also bemoaned his side's lack of fortune as France's opener came via Mario Mandzukic's own goal.
Despite having played 90 extra minutes than Les Bleus over the course of the tournament in three periods of extra time, and having a day's less rest before the final, Croatia dominated the first-half.
Perisic deservedly equalised and Griezmann's penalty was France's first shot on target.
France's pace on the counter-attack proved too much in the second period, though, as Paul Pogba and Kylian Mbappe added to their lead before Mandzukic pounced on an error from Hugo Lloris for a consolation.
"On our bus there is a slogan: "small country with big dreams". That's a good message to all," added Dalic.
"You should never give up, never stop believing. At 4-1 down I was not defeated. Overall, Croatia played a great tournament and showed its strength and quality.
"I would like to thank all my players for what they have done. Having a look back, I am proud."
Croatia did at least win one prize as captain Luka Modric was rewarded for his outstanding tournament with the Golden Ball for the World Cup's best player.
"We are very glad for Luka Modric to have won the Golden Ball, deservedly so, and he played a terrific tournament," said Dalic.
"That's another commendation for the team. He did the lion's share of the work in our play and deserved the Golden Ball although we did not win."
And with his reputation now sky-high, he said he will take time to consider his future.
"I will take time out," he added. "At this moment I'm not thinking about anything other than going back to Croatia and having a rest."
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)