Watson, coming off a first-round loss to Irina-Camelia Begu in Indian Wells, suffered another failure at the first hurdle despite dominating the opening set against the world number 50.
Morita broke on two occasions to Watson's one to edge a close second set before the same pattern was repeated in the decider as the Japanese ran out a 1-6 7-5 6-4 winner in two hours 45 minutes.
The loss continues a miserable sequence for 20-year-old Watson, who has yet to win a match since climbing to a career-high 39 in the world rankings last month.
"This year I've been going a bit too long so I'm a bit burnt out," Watson said in quotes reported on the BBC Sport website.
"I've been thinking about it for a while now and I'm definitely going to take a break from tennis."
Watson's Indian Wells conqueror Begu had no such trouble as she won her opener 6-1 4-6 6-4 against New Zealand's Marina Erakovic, while China's Peng Shuai defeated Sofia Arvidsson of Sweden 6-3 6-2.
Flavia Pennetta is safely into the second round after a routine straight-sets victory over Sweden's Johanna Larsson, the Italian prevailing 6-4 6-1.
Hsieh Su-wei of Taiwan won a hard-fought second-set tie-breaker on her way to a 6-4 7-6 (17/15) victory over Lesia Tsurenko of Ukraine, while France's Kristina Mladecnovic was a 7-5 6-2 winner against Canada's Aleksandra Wozniak.
Kimiko Date-Krumm of Japan swept aside South Africa's Chanelle Scheepers 6-2 6-0, and Croatian wild card Ajla Tomljanovic made light of a 143-place rankings gap in her match with Kazakhstan's Ksenia Pervak, the world number 242 prevailing 6-2 6-2.
Holland's Kiki Bertens is also through after Georgia's Anna Tatishvili retired with an ankle injury when trailing 0-6 0-1, while in the day's final match German wild card Andrea Petkovic saw off Serbia's Bojana Jovanovski 6-3 6-1.