Pulis, Rodgers managers of the year
Rodgers' award was voted on by all LMA members, including every manager in the top-four professional leagues in English football. Pulis' award is specific to the Premier League only.
Rodgers, who hails from Northern Ireland, was honoured for the first time at the annual awards dinner in London after he led the Reds to second place in the Premier League, which was the club's highest finish in five years.
LMA chairman Howard Wilkinson said of Rodgers' win: "There can be no greater tribute to a manager and his work than a tribute awarded by his match day foes and peers. This evening we applaud Brendan Rodgers as he receives that most valuable award.
"Liverpool Football Club's performances and results this season have provoked memories of some of those momentous years in the past when they had to contend with those two United's, the first from Leeds, the second from Manchester.
"For Liverpool and Brendan, I'm sure we all hope this season marks the beginning of a new voyage and a new era."
Pulis' work at Palace saw the club keep their top flight status after the former Stoke boss guided them to an 11th place finish. When Pulis arrived at the club, Palace had just four points but they finished the season with a haul of 45 and steered well clear of a relegation that looked certain earlier in the year.
He told his club's official website: "This is a community club based in the most densely populated area in London and has a great opportunity of pushing forward. We've got to stay in the Premier League for the next two or three years to realise what we can eventually achieve. We have to look forward and say this is the way we will go and do it."
Leicester manager Nigel Pearson won the Sky Bet Football League Championship Manager of the Year award after he steered the Foxes to automatic promotion to the top flight, while Wolves' Kenny Jackett and Leyton Orient's Russell Slade were named joint League One Managers of the Year.
Scunthorpe's Russ Wilcox picked up the League Two award with Sheffield United's Nigel Clough named the FA Cup Manager of the Year.