Radwanska led Tsvetana Pironkova by a set and 3-0 when play was halted on Sunday, but lost 10 games on the resumption and was beaten 2-6 6-3 6-3.
She said a previous hand injury meant the heavy conditions made it impossible for her to play her game.
“I had surgery a few years ago and I couldn’t really play in those conditions, end of story,” said the second seed.
“I’m just so surprised and angry we have to play in the rain. I mean, it’s not a 10,000 tournament (the lowest level of professional tennis). It’s a grand slam. How can you allow players to play in the rain? I cannot play in those conditions.
“I don’t know who allows us to play in these kind of conditions. I don’t think they really care what we think. I think they care about other things, I guess.”
Roland Garros witnessed its first total washout in 16 years on Monday and organisers were desperate to avoid the same situation for a second day.
The rain was not as heavy yesterday, but was persistent. The players resumed their matches just after midday and played for nearly 40 minutes before being taken off once more.
There followed another two-hour delay before the matches were called again, despite the ongoing drizzle.
Halep had led Sam Stosur 5-3 on Sunday but, like Radwanska, was on the back foot from the start yesterday and went down 7-6 (7/0) 6-3.
The sixth seed and 2014 finalist said: “I cannot comment about the conditions, I have no words. It was impossible to play, in my opinion. And to play tennis matches during the rain, I think it’s a bit too much.
“No one cares about the players, in my opinion. I don’t care that I lost the match today, but I was close to getting injured with my back, so that’s a big problem. But, like I said, no one cares. We have just to go and play.
“The court was not good. The balls were wet, completely wet during the match. I felt some pain in my back, in my Achilles. Sam was stronger and she played better today, and these conditions I think are good for her because she has a lot of topspin.”
Asked why she thought play continued despite the conditions, Halep said: “Maybe they are scared because the days are going on and they don’t play matches. But it’s not our fault. It’s not their fault. But the decisions were not, I think, the best. I didn’t feel sure on court, safe on court.”
Several men’s fourth-round matches were also affected. David Goffin and Ernests Gulbis took matters into their own hands and refused to continue their match, while Dominic Thiem also walked off during his contest with Marcel Granollers.
Asked if she could have done the same, Halep said: “I’m not that kind of person and I will never do that.”
Stosur was beaten in the final by Francesca Schiavone in 2010, but had not been beyond the fourth round here since 2012.
The Australian, who now plays world number 102 Pironkova, said of the conditions: “I know what it feels like out there and I know it was raining for the first time we went out today, but the court was okay for the most part.
Pironkova is renowned as a dangerous player on fast surfaces, particularly grass, but her run to the last eight has been a complete surprise.
The Bulgarian, who had never previously been beyond the third round at Roland Garros, joins American Shelby Rogers to make it two players ranked outside the top 100 in the last eight.
Meanwhile Novak Djokovic faces a hectic schedule if he is to win his first French Open title after another sodden day at Roland Garros.
The world number one was unable to go on court for his fourth-round match against Roberto Bautista Agut on Monday and the pair only managed two-and-a-half sets yesterday.
Djokovic recovered from losing the opening set for only the fourth time in a slam in two-and-a-half years in damp, heavy conditions to lead 3-6 6-4 4-1 when conditions were finally deemed unplayable.
Just before 7pm local time, play was called off the day, meaning Djokovic faces having to play four times in five days if he is to lift the one grand slam trophy to elude him. .
Djokovic made the perfect start against 14th seed Bautista Agut, breaking the Spaniard’s serve, but he struggled to hold his own and was broken three times in the opening set.
The end of the first set brought another lengthy rain delay and, even when the players were called back to court around two hours later, it was clear organisers were far from sure the conditions were playable.
Djokovic and Bautista Agut were made to wait in the corridor leading to Court Philippe Chatrier while drizzle fell. Djokovic ventured onto court and borrowed a fan’s umbrella, giving it a twirl as he inspected the court.
Finally the match resumed and Djokovic seemed determined not to let the weather bother him. He won the first seven points but it was not until the sixth game he finally broke Bautista Agut’s serve.
The balls were soon clay-coloured and both men were struggling to hit through the heavy conditions. Five consecutive breaks of serve eventually ended with Djokovic winning the second set.