The 41-year-old is adamant that his side can still attract top players to Anfield this summer - despite losing out on the Chile international to the Gunners
The Chile international completed his €40 million move to Arsene Wenger’s side earlier this month, although Liverpool were in the running for the forward’s signature.
Liverpool have already completed moves for Rickie Lambert, Adam Lallana, Emre Can and Lazar Markovic this summer and Rodgers’ insists his side have no problem when attempting to attract high-profile players.
“I don’t think so,” Rodgers told reporters.
“That was one [Sanchez] where geography dictated where he wanted to go - simple as that. It’s been the other way.
“Lots of players are really impressed by what we are doing as a club and really excited about coming to Liverpool.
“It wasn't due to a lack of ambition by the club. It was about where the player and his family wanted to choose to live.
“He’s a fantastic player and would have suited us. His profile would have been great but it was not to be and we move on.”