By failing to reach the last four, Wozniacki is guaranteed to lose her number one spot to Azarenka, Petra Kvitova or Maria Sharapova when the new standings are released next Monday.
But the defiant Dane, who lost her only grand slam final to Clijsters at the 2009 US Open, backed herself to return to the top by the end of the year.
"You know, to be honest, I don't really think about it," Wozniacki said. "I have been there for a long time already. I finished number one two years in a row.
"We are just in January. In the end of the year you see who has played the best, most consistently all year round. I will get it back eventually, so I'm not worried."