The 36-year-old Spaniard was pushed to the limit and beyond in what was his first match since an abdominal tear forced him out of Wimbledon.
Croatia's Coric, who also withdrew from Wimbledon due to injury, started strong against the world number three, absorbing Nadal's best shots and returning them in kind.
Both men saved two set points before the 25-year-old claimed first blood in a lengthy tiebreak.
Nadal then rallied in the second, making the most of his lone break point opportunity to force a deciding third set.
However he was ultimately unable to keep up with his younger opponent in the third, giving up an early break which Coric rode to a 7-6 (9) 4-6 6-3 victory in Cincinnati.
"Obviously I didn't play my best match," Nadal said in his post-match presser.
"[It is] something that can happen. Historically this tournament has been difficult for me. So coming back from a tough period of time, [it is] something that's easy to accept and easy to say congrats to Borna, that he played better.
"It's difficult to take a lot of positive things, but I need to improve," Nadal added.
"I need to practise. I need to return better. I need days [on the court], and that's the truth.
"Obviously I had my chances in the beginning. In the tie-break I had two important chances with two set points that I played terrible with two more-or-less easy shots."
The 36-year-old also admitted to playing "a couple of terrible points" after he created an opening at 0/30 early in the third set, but at this stage in his career Nadal is no stranger to coming back from a setback.
"You lose, you move forward. I know the way," he said. "The main thing for me is stay healthy.
"It has been a difficult injury to manage, to be honest.
"The last month and a half hasn't been easy, because having a tear on the abdominal, you don't know when [you are]100 per cent over the thing, so that affects a little bit in terms of not [being] sure if you are able to try your best in every serve."
The next time we see Nadal in action will be at the US Open at the end of the month.
"I need to move forward and just start to think about the energy that the crowd gives me in New York," he added.
"I know it's a very special place for me, and I enjoy it. [I've had] unforgettable moments there, and I'm going to try my very best every single day to be ready for that."