British number two Watson, 24, took the first set against Magdalena Rybarikova but went down 4-6 6-0 6-4.
Robson, 22, had her serve broken six times as she lost 6-3 7-5 to Portugal's Michelle Larcher de Brito.
Naomi Broady bowed out after a 6-2 6-1 loss to Su-Wei Hsieh, but British number four Tara Moore progressed by beating Croatia's Donna Vekic 6-2 7-5.
The 23-year-old joined British number one Johanna Konta in the second round, after Konta triumphed 6-3 6-0 over American Victoria Duval on Monday to set up a tie with China's Zheng Saisai.
Moore will play American eighth seed Christina McHale on Thursday, having won only her second match in the main draw of a WTA event.
The world number 280 won an ITF event in Eastbourne last week, but may need a wildcard to play at Wimbledon.
"I'm still in the tournament here so I am just going to look forward to the next match I'm playing," she said.
"As far as the next few weeks go, I'm not sure yet. I have put in a request but it's not my decision. It's the All England Club's decision and I respect the decision."
Former world number one Caroline Wozniacki also reached the second round with a 7-5 6-3 win over Cagla Buyukakcay, but fifth seed Yanina Wickmayer was defeated 7-5 7-6 by 'lucky loser' Andrea Hlavackova.
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Great Britain's Heather Watson and Laura Robson were knocked out in the first round of the Nottingham Open.