Britons Heather Watson and Naomi Broady failed to qualify for the Madrid Open.
Watson, ranked 19 places higher than Mirjana Lucic-Baroni at 56, led by a break in the first set but the Croat came back to win 7-6 (7-4) 6-2.
Broady, the British number three, lost to Puerto Rico's Monica Puig, who won 3-6 6-3 6-3 in a match lasting two hours and seven minutes.
Laura Robson will take on Victoria Azarenka in the main draw after using her protected ranking of 58 to enter.
The 22-year-old missed 17 months with a wrist injury, and has won just one WTA main draw match since returning last summer.