She probably wasn't as sleepy as she was trying to appear, but the fact that he seemed to accept her response meant that she didn't have to fake it. Or perhaps he was eager to be rid of her, at least for the night. Perhaps he wasn't at all endeared to her drunken antics; Sasha tended to not like others when they were drunk, so she certainly wouldn't blame him.
"Oh no, I couldn't, the couch is fine, I don't want to inconvenience you." In all honestly, she'd have felt a bit weird to be sleeping in the bedroom of a man she barely knew, even though she wasn't sober enough to be worried about the dangers of staying over with an acquaintance she didn't intend to sleep with. But even if she hadn't felt weird about it, she still wouldn't have wanted to put him out. He hadn't asked for this, he shouldn't have to give up his bed for a drunk girl.