Needing a draw to progress to the knockout stage for the first time, India finished bottom of Group A after conceding an injury-time penalty that allowed Bahrain to leapfrog them into third place.
The All India Football Federation (AIFF) confirmed on its Twitter account that the former Millwall coach, who took over the job in 2015 for a second stint with the team, had stepped down.
"We haven't received any official communication from him yet but we accept his decision & thank him for his contribution to #Indianfootball," AIFF general secretary Kushal Das was quoted as saying.
Constantine said he was stepping down having achieved the target of helping India qualify for the continental showpiece after an eight-year gap. The side also broke into the top 100 in the FIFA rankings last year.
"My objective from day one was to qualify for the Asian Cup," the 56-year-old Englishman, who first coached India from 2002-2005, told reporters after the match.
"I've done that and I'm exceptionally proud of the players for everything they have given.
"I think my cycle has finished. I did what I was asked to and a little bit more and, after four years, it's time to leave.
"I'm sad to be leaving, the players and staff have been fantastic throughout ... even those who failed to make the final squad.
"It's my wife's birthday today and I haven't been back to my house in six years. I've only seen my three daughters every three or four months and the time has come for me to move on."
Constantine's team started well thumping Thailand 4-1 but defeats by hosts United Arab Emirates and Bahrain dashed their hopes of making the knockout stage for the first time.
Hosts United Arab Emirates topped the group ahead of Thailand following their 1-1 draw. Both teams advanced to the knockout stage while Bahrain also progressed as one of four best third-placed teams.
(Reporting by Amlan Chakraborty in New Delhi; addition reporting by Ahmed Maher and Rohith Nair; editing by Nick Mulvenney/Greg Stutchbury)
