There appears to be quite a long list of players Rodgers wanted that, for whatever reasons, we didn't get. Some, like Dempsey, we can be thankful for, but we'd be a better side by miles if players like Williams, Delle Ali and Sanchez were Liverpool players. Mind you, it would also be a better team if they'd blocked him from signing the likes of Joe Allen, Borini, and arguably Benteke too, so again, it's hard to call.
(I'm not laying blame for Sanchez at anyone's door, that's not really down to any lack of effort, simple player preference)