Then why would she say “There was no father. I carried him, I gave birth to him, I raised him. I can’t explain what happened.” Rather than “His father left (or died) before he was born”, or “His father was a spacer passing through and I never saw him again”, or something like that.
If you take the new EU novels as canon, you could argue that Anakin’s father was Darth Plagueis, who had been experimenting with creating life through the Force around the time of Anakin’s conception.
Then why did she say “I can’t explain it.”?
“I don’t know who the father is” is really easy explanation if the father is an unknown person. Or “his father wasn’t around and I raised him myself”. Or maybe “I don’t want to get into it” if it was an unwilling pregnancy related to her status as a slave
“I can’t explain it” implies she can’t trace it back to a person (or group of people) at all.
Anakin not having a biological father is a major factor in the council seeing him at all despite his being already “too old” for training according to Yoda. If he weren’t unique the council wouldn’t have wasted their time with him and just rejected a meeting all together.