The Reds boss scooped the accolade last week after leading his side to within touching distance of their first league title for 24 years.
The Anfield outfit finished seventh in the 2012-2013 campaign, before jumping to second last season, eventually finishing two points behind Premier League champions Manchester City.
Rodgers has also overseen remarkable improvements in several players at the club, including Jordan Henderson and Raheem Sterling, and the pair will be part of England's World Cup squad in Brazil alongside club teammates Steven Gerrard, Daniel Sturridge and Glen Johnson, while Jon Flanagan has been named in the seven-man backup list.
Speaking to LFC.tv, in an interview that will be broadcast later this week, Rodgers spoke of his pride at being the recipient of this year's award, and said it was something he had worked towards for the past two decades.
He said: "I never had a big career as a footballer, so I knew I would be on a different pathway to most coaches. I didn't need to be liked, my only concern was that I could be respected for my work.
"And the award the other night went a long way to when I first started 20 years ago, as a symbol of respect. I was very proud to be voted for my work at Liverpool. I was extremely proud and very honoured as you can imagine to pick up the award.
"I remember being a manager for about five years and I went to my first LMA awards [ceremony] and seeing all the great managers that had won the award in the past, and you always hoped [one day] you'd done a job worthy of your peers.
"It's the same for the players, because the biggest compliment you can get is from people in your own industry. When I started as a coach nearly 20 years ago, my objectives were simple; I wanted to make people better, I wanted to help them in their life, football and social life. How could I help them become better? And my other objective was to earn respect."
Despite the disappointment of missing out on the title on the final day of the season, Rodgers' Reds will take comfort from the fact that they will return to the Champions League for the first time in five years next term.