Nadal was ambushed 7-6 (11/9), 4-6, 6-3 in his second-round start by Croat Borna Coric, ending his hopes of overtaking Daniil Medvedev for the world number one rankings.
Top seed Medvedev, who plays on Thursday for a quarter-final spot against Denis Shapovalov, can tighten his grip on his current top position heading into the US Open.
Third-ranked Nadal was rocked by his loss after six weeks away as he healed an abdominal muscle injury that forced his withdrawal from a Wimbledon semi-final against Nick Kyrgios.
Now Nadal goes into the US Open, which begins on August 29 in New York, with only one summer hardcourt match.
"In terms of New York, it's a Grand Slam, a different kind of tournament," Nadal said.
"I was only able to play two sets before this match in the last 40 days.
"I know that to gain condition. I will have to (be) on the tour practicing with the guys (other players)."
The 36-year-old Spaniard with 22 Grand Slam titles said he hopes to feed off fan energy at the US Open, where Nadal won titles in 2010, 2013, 2017 and 2019.
"There is an energy the crowd gives me in New York. It's a very special place for me," Nadal said.
"I've had unforgettable moments there and I'm going to try my very best every single day to be ready for that."
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)