Poulter lost to Thomas Aiken 1 up at the Thracian Cliffs course, bogeying the last hole after missing the fairway.
"I have no excuses," Poulter said. "There is no excuse for that display of golf over the last two days. It's disgusting, disgraceful and there's no explanation. I should have been able to finish the match off."
Poulter lost to Thongchai Jaidee on Thursday. On Friday morning, Jaidee beat Aiken 1 up.
Jaidee is one of only four players to win both early matches, joining Francesco Molinari, Gonzalo Fernandez-Castano and Scott Jamieson.
Fernandez-Castano beat Jamie Donaldson on Friday and then defeated Brett Rumford 3 and 2.
Rumford won his opening match earlier in the day, beating Jamie Donaldson 5 and 3 Friday.
"Jamie got off to a bit of a bad start and I just capitalized on that with three birdies in my first four holes to be 3 up and that really was the key," Rumford said.
Richard Sterne also ensured his advancement by defeating former U.S. Open champion Geoff Ogilvy 5 and 4, while defending champion Nicolas Colsaerts recovered from his first round loss, beating Kiradeck Aphibarnrat 3 and 2.
"It played a little better today but there are still a few loose shots in my game, but I needed to win so I guess it's mission accomplished," Colsaerts said. "But hey, I'm in a better spot this year than compared to this time last year when I managed to go through to the last 16 with just a draw from my first two matches."