The winner of a men's record 22 Grand Slam championships, including two this year, hadn't played since July 6 after an abdominal tear forced him to withdraw from a semifinal match against Nick Kyrgios at Wimbledon. He was hoping to start putting the final touches on prepping for the upcoming US Open.
"With a week-and-a-half to New York, it's sad to not play here,'' Nadal said. "I need to get into Grand Slam mode."
The second-seeded and third-ranked Nadal, 36, showed no signs of the injury that mostly plagued his serve. He reached 121 mph with one serve and needed several awkward body movements to return some of Coric's shots.
"I need to practice,'' Nadal said. "I need to return better. I need days. It's better to come back when you've spent a period of time outside and win your first match. I wasn't ready enough to win the match today. The big thing is to stay healthy. It's a difficult injury to manage. I need to take it step by step.''
The match lasted 2 hours, 51 minutes, not including a rain delay of 1 hour, 25 minutes in the first set.
Also, Taylor Fritz beat Kyrgios 6-3, 6-2, and 19-year-old wild card Ben Shelton upset fifth-ranked Casper Ruud. Shelton is the youngest American to defeat a top-five opponent since Andy Roddick beat No. 1 Gustavo Kuerten in 2001.
Sebastian Korda came back to defeat Frances Tiafoe 4-6, 6-1, 6-4 to reach the third round in Cincinnati for the first time. He is among four American men to advance to this stage of the tournament, the most since 2003 when there were five; he joins Fritz, Shelton and John Isner, his next opponent.
The Associated Press contributed to this report.