Ramkumar, who ended a runner-up at the Newport event last week, lost 4-6, 4-6 to American Taylor Fritz.
AITA usually names five-member squad apart from one or two reserve players.
World No 15 India will now compete in the Zone Group action later this year.
Leander Paes is set to return to the Indian Davis Cup squad after making himself available for the upcoming tie against Pakistan as the country's top players and non-playing captain Mahesh Bhupathi have refused to travel to the neighbouring nation, citing security concerns.
Spectators were on their feet cheering Leander Paes who in all probability is playing his last ATP event on Indian soil.
Surprisingly, Yuki Bhambri has preferred a smaller $50,000 Challenger tournament in Kobe, Japan, while Ramkumar Ramanathan has to attend a mandatory ATP educative programme in London.
Following is the schedule of Indian contingent on the fifth day of the Asian Games.
Mahesh Bhupathi rued that his men failed to seize the opportunities against a much higher-ranked Italy
Monday was also the first time in more than two decades that India had more than one player in the main draw of a Grand Slam singles, with Prajnesh Gunneswaran losing to world number five Daniil Medvedev in an earlier match.
A summary of sports events and persons who made news on on Thursday
Bindra realistic after the Haryanvi takes a set off Federer in US Open first round.
Australia eased ahead of Bosnia 2-0 as John Millman thumped Damir Dzumhur 6-3, 6-2 while Alex de Minaur overcame Mirza Basic 6-3, 7-6(0), before Millman revealed the team's larger goal under captain Lleyton Hewitt.
Win is the only thing on Seppi's mind and he is focussed on giving his country the lead on Friday.
Zeeshan Ali, the captain and coach of the men's team, has no clue about Paes's arrival three days before the start of the competition on Sunday.
In a big setback to the Indian Davis Cup team, country's leading singles player Yuki Bhambri was, on Sunday, ruled out of the upcoming tie against Uzbekistan due to a knee injury.
No Indian Davis Cup squad has travelled to Pakistan since March 1964 and in that tie, held in Lahore, India had won 4-0.
Ramkumar Ramanthan gave his all but it was not enough to stop Laslo Djere from winning his first Davis Cup match as India trail Serbia 0-1 in the World Group Play-off tie, in Kraljevo, Serbia, on Friday.
Veteran tennis player Rohan Bopanna said he plans to team up with Divij Sharan and represent India in the men's doubles event in next year's Tokyo Olympics.
Bopanna being the highest-ranked doubles player in the country is automatic choice for the doubles rubber.
Summary of sports events and persons who made news on Friday
Serbian Djokovic, 31, needed elbow surgery in February to cure a problem that surfaced in 2017, but after some jarring defeats he returned to the kind of domination he achieved in 2015, winning Wimbledon and the US Open.
Wawrinka splits with long-time coach Norman
A summary of sports events and persons who made news on Friday
Rohan Bopanna and Divij Sharan used all their experience to bounce back and enter the men's doubles final of the Asian Games, in Palembang, on Thursday.
Yuki, ranked 93, has told AITA that if he gets direct entry into the last Grand Slam of the season, he won't be available.
A summary of sports events and persons who made news on Monday
AITA won't force any player to travel to Pakistan and is willing to send even a second-string team to avoid suspension
According to the latest rankings issued on Monday, the left-handed Sharan is ranked 50th after gaining a place. He had reached the final of the last three tournaments he participated in, winning the ATP 250 European Open, while ending runner-up at Challenger events in Brest and Tashkent with different partners.
'I still have the exact budget which I had in 2018 when I was ranked 350. It's that when I needed the most which is right now, I see people turning around and walking away.'
India's number one singles player Prajnesh Gunneswaran beat Jay Clarke of Great Britain in straight sets to enter the main draw of the Miami Open, on Wednesday.
India's big hope Yuki Bhambri crashed out of the US Open men's singles qualifiers with a three-set defeat to Japanese Go Soeda while Prajnesh Gunneswaran also suffered a tame defeat in New York.
World No. 16 Marco Cecchinato will spearhead Italy's challenge, while they also have the experienced world No. 37 Andreas Seppi as they look to continue their good record against India.
Sumit Nagal lived a dream when he took on one of the greatest players of all time at a packed Arthur Ashe stadium in a US Open first-rounder.
Bopanna also in reserves while four single specialists named in squad
Senior pro Leander Paes's place in the Indian Davis Cup team will be up for discussion when the AITA Selection Committee meets on Monday to pick the squad for the upcoming Asia/Oceania Zone tie against Uzbekistan.
At one stage Yuki was a break up, serving for the opening set but lost his serve and eventually the set. After drawing parity, Yuki twice lost his serve to fall behind 0-3 in the decisive set and never recovered.
'The only thing I am feeling bad right now is, if he had decided earlier to not come even two weeks or 10 days ago, we would have got a specialist doubles team in place'
Andreas Seppi experienced some early hiccups before getting past Ramkumar Ramanathan 6-4, 6-2 in the opening rubber, while 22-year-old Matteo Berrettini made a winning Davis Cup debut, cruising past India number one Prajnesh Gunneswaran 6-4, 6-3.
Summary of sports events and persons who made news on Wednesday
Summary of sports events and persons who made news on Tuesday