The Anfield club were reported to have made the first approach for the Brazilian winger, however late bids from Tottenham and Chelsea appear to have taken the player away from Rodgers.
But while the Northern Irishman admitted that he was disappointed not to have signed the 25-year-old, he questioned the reasons behind the player's choice.
"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.
Chelsea are thought to now be leading the race for his signature, despite the Brazil international having reportedly had a medical ahead of a proposed £30million move to Tottenham.
