Djokovic had given his side hope of reaching the final after winning the second singles rubber against Marin Cilic 6-4 6-2.
World number 279 Borna Gojo continued his dream Davis Cup week as he came from behind to beat Dusan Lajovic 4-6 6-3 6-2 and get the Croatians off to a flying start.
Djokovic’s win ensured the tie would come down to a battle between the accomplished Croatian duo and Djokovic and partner Filip Krajinovic.
The Croatians came through a tight first set and a break for the favourites early in the second gave Djokovic and Krajinovic a tough task to keep Serbia’s hopes alive.
But ultimately the Croatians’ experience told and their 7-5 6-1 win wrapped up a 2-1 win and a place in Sunday’s final against either Russia or Germany.
It marked a disappointing end to the season for Djokovic, who had missed out on a calendar grand slam at the US Open, and was also dumped out of the ATP Tour finals at the semi-final stage.
But the 34-year-old said he had no regrets about the way his season had ended, and said he would learn from experiences like the “cruel” loss to the Croatians.
Djokovic said: “I gave my best for the national team, there is extra meaning and importance for me, and unfortunately it wasn’t to be this time.
“As much as it hurts me personally and as a team, these are usually the biggest opportunities to get stronger, to grow and to develop as a person and a player.
“One singles win is not enough. This kind of competition is cruel in a way because it requires you to win every single match that you play, or every single set.
“I don’t regret anything in life. I try to draw lessons from tough moments like this.
“As much as it hurts me personally and as a team, these are usually the biggest opportunities to get stronger, to grow and to develop as a person and a player.”
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