The Reds had been hopeful of securing a deal for the 25-year-old, but the Brazilian will not be joining the club following interest from Tottenham and Chelsea
The Anfield club were reported to have made the first approach for the Brazilian winger, but were gazumped by Tottenham before a late bid from Chelsea ensured Rodgers missed out on the former Shakhtar Donetsk man.
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"It’s disappointing because this was a player who would have been perfect for us," Rodgers admitted. "It wasn’t a football [decision] and I don’t really want to go into it… that’s for us as a club really.
"The bottom line is he hasn’t come here for whatever reason and we move on.
"We identify the targets and then try and get the deal done financially. That’s how it was.
"The club has pushed financially as hard as they felt they could but it wasn’t to be."
Willian only signed for current club Anzhi Makhachkala in January but has now been made available for transfer after the Russian outfit moved to off-load some of their top earners.
Jose Mourinho has confirmed that Chelsea are now leading the race for the Brazilian's signature, despite the playmaker having had a medical with Tottenham.