The 21-year-old Alcaraz had been attempting to become the youngest Olympics men's singles champion of all time, but described his loss as "painful" as he broke down in tears on court as he attempted to conduct a TV interview.
"I feel that I let the Spanish people down. I feel they were waiting for the gold medal," said Alcaraz after his 7-6 (7/3), 7-6 (7/2) defeat.
"I got emotional because I couldn't make the Spanish people proud. That's (why) I got emotional."
Victory would have continued Alcaraz's golden summer in which he won a first French Open on the same Roland Garros courts which hosted the Olympics and then successfully defended his Wimbledon title by sweeping Djokovic off the court last month.
In Sunday's final, which stretched to almost three hours, neither player dropped serve with a total of 14 break points carved out and successfully saved.
Alcaraz saw eight break points come and go on Court Philippe Chatrier.
"I'm a bit sad but I did a great tournament. It was a really great match and I'm really proud of myself," he added.
"I was facing a hungry Novak, he was very impressive today. He didn't let me have many chances so credit to him and he deserves victory."
Despite his disappointment, Alcaraz said he will learn from Sunday's loss as he heads to North America and an assault on the US Open which he won in 2022.
The New York title is the only Grand Slam crown currently in the possession of Djokovic.
"I'll leave with my head held high," said the Spaniard.
"Last year, when I lost to Novak at the French Open, I said I'd learn from that. I will learn from this again, become a better player and not make the same mistakes. I will be more mature."
Alcaraz said the Paris Olympics will remain a special memory especially as it gave him the chance to play doubles with Rafael Nadal for the first time.
"The tournament has been really special for me and I will remember it for the rest of my life," he said.
