The unseeded Indian was serving for the match at one stage, but eventually lost 7-6 (5) 3-6 5-7 in the second round, which lasted two hours and 37 minutes.
Ramkumar, who shocked world number eight Dominic Thiem at Antalya Open last week, broke his rival in the sixth game of the third set to take a 4-2 lead, but failed to build on the advantageous position.
The 22-year-old handed back the momentum to Caruso by immediately dropping the serve in the seventh game, but snatched back the advantage by breaking the Italian in the next game.
It was back on serve at 5-5 and it was imperative to hold serve, but the Indian dropped guard in the 11th, allowing his rival to emerge victorious.
Caruso will next face the winner of the match between French fourth seed Kenny De Schepper and Italian Andrea Arnaboldi.
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