How did Rodgers do "a better job"? Got Liverpool to the top of the league and then failed to set his team up properly against Chelsea and chucked it away? Shipped 3 goals against Palace? Yeah, Liverpool played some great football, but their defensive issues cost them the league and that's on the manager's hands.
Poyet and Pullis both did tremendous jobs, fair enough. I wouldn't be disappointed to see either of them win it. But of the 'big' managers ol' Manuel did the best job: he won the league. And wasn't a tosser whilst doing it.