The LMA also honoured Crystal Palace boss Tony Pulis with the Premier League Manager of the Year award for an impressive six months in which he replaced Ian Holloway mid-season and pulled the club out of relegation danger.
Liverpool, after finishing seventh a year ago in Rodgers' first season in charge, had been in pole position to win the title before late slip-ups to Chelsea and Crystal Palace saw them finish second, two points behind Manchester City.
"There can be no greater tribute to a manager and his work than a tribute awarded by his matchday foes and peers," LMA Chairman Howard Wilkinson said of the award, voted on by all coaches in England's four professional leagues.
"For Liverpool and Brendan, I'm sure we all hope this season marks the beginning of a new voyage and a new era."
Under Welshman Pulis's watch, Palace went from strength to strength, finishing 11th after a five-match winning streak and only one loss in their last eight games.
"We finished sixth in the Championship last season and 11th in the Premier League this season. That's a 15 place jump!" British media quoted Pulis as saying at the awards ceremony.
"This is a community club based in the most densely populated area in London and has a great opportunity of pushing forward," he said on Palace's website (www.cpfc.co.uk).
"We've got to stay in the Premier League for the next two or three years to realise what we can eventually achieve."