British number two Heather Watson and Harriet Dart narrowly lost their first-round matches at the Eastbourne International.
Watson, 29, had led 4-1 in the decider against fourth seed Iga Swiatek but was beaten 6-3 6-7 (4-7) 7-5.
Earlier, Dart also fought back against Elena Rybakina but was defeated 6-2 6-7 (5-7) 6-4.
In the upset of the day, defending champion Karolina Pliskova lost 2-6 6-2 6-2 to Italian qualifier Camila Giorgi.
Watson came into this tournament with a lot of confidence, having reached the semi-finals in Birmingham last week, and started confidently against Polish world number nine Swiatek.
In one lax service game, Watson double-faulted three times to gift a break and ultimately the first set to the 20-year-old 2020 French Open champion.
Watson held her nerve to force a tie-break in the second set, taking charge as Swiatek struggled with her shot-making.
The British world number 65 went a double break up in the deciding set, but the Pole gradually turned the tables, breaking Watson three times for her first main-draw win on grass.
Dart & Pliskova beaten but Svitolina advances
British number three Dart, 24, saved a match point in the second set against Kazakhstan's Rybakina.
But Rybakina, 22, who had looked to be struggling with a foot problem, rallied to break Dart twice in the decider.
There was disappointment for two-time champion Pliskova, who started well against Italian qualifier Giorgi but lost 2-6 6-2 6-2.
The Czech fifth seed, 29, will now fall out of the top 10 in the rankings for the first time in nearly five years and heads into next week's Wimbledon without a win on the grass this season.
Second seed Elina Svitolina was in danger of an early exit but came from behind to beat Spain's Paula Badosa 4-6 6-1 7-6 (7-1).
The 26-year-old Ukrainian has never been past the second round at Eastbourne.
In the men's tournament, Britain's Jay Clarke lost 6-3 6-2 to Australia's John Millman.
Liam Broady and James Ward are also due to play their opening matches later on Tuesday, which features a packed schedule after play was washed out on Monday.
Djokovic warms up with doubles win
In Mallorca, at one of the other grass-court events where players are getting ready for Wimbledon, world number one Novak Djokovic was in action in the doubles.
The Serb, who will be defending his Wimbledon title and chasing a 20th Grand Slam, partnered Spain's Carlos Gomez-Herrera in a 5-7 6-4 13-11 win over Nikola Cacic and Tomislav Brkic.
In the singles at the same event, Russian world number two Daniil Medvedev beat Corentin Moutet 6-4 6-2 to reach the quarter-finals, but Austrian world number five Dominic Thiem was forced to retire from his match against Adrian Mannarino with an injury.
Thiem had been leading 5-2 in the opening set when he struck a forehand and appeared to hurt his right wrist. He had a medical timeout before retiring from the match.Live scores, results and order of playAlerts: Get tennis news sent to your phone