Denesh Ramdin's side completed a 3-0 one-day whitewash of Bangladesh on Monday but West Indies are ranked a lowly eighth in both the ODI and test rankings.
Sweeping changes were made behind the scenes earlier this month with Lloyd taking over as chairman of selectors from Clyde Butts and being joined by new panel members Courtney Walsh and Eldine Baptiste.
Greenidge, who used to play alongside pacemen Walsh and Baptiste and was an important cog in the wheel when West Indies ruled world cricket under Lloyd's captaincy, said he hoped the new chairman would be treated with the respect he deserved.
"The powers-that-be need to accept Clive, appreciate him and look upon him as the person he is, someone who can get the job done," Greenidge told Reuters in an interview.
"I feel in recent times there has been a lot of disrespect shown to players who have played in the past and there has been more dictatorial behaviour happening around cricket in the Caribbean.
"I haven't been involved for a while which is a damned shame because a lot of players who played in the past have got so much to contribute and have not been given a chance to do so," added the former swashbuckling opener.
"I just hope they recognise Clive's contribution to the West Indies and give him the necessary tools to work with. I don't see a problem at all with Clive but it may be a problem with the people he's working with or the people he reports to."
Greenidge said there were similarities in the turmoil that has been experienced at Manchester United since Alex Ferguson ended his all-conquering 26-year managerial reign at one of the world's most famous football clubs in 2013.
Asked if Lloyd needed to be given a free rein to do the job as he saw fit, Greenidge was emphatic in his reply: "Precisely.
"It's a bit like what's happening at Manchester United. Everyone's expecting the new managers there to just pick up where Alex Ferguson left off - that's impossible.
"The new man needs to transfer a serious input of his thinking to his team and the way he wants them to go. He needs to build a team and explain how he wants them to go forward.
"It's the same thing with Clive Lloyd," added Greenidge who hit 19 centuries for West Indies in 108 tests between 1974-91.
"Unfortunately his job will be measured in terms of how successful the West Indies team is, that's always been the case, but I think a change around is necessary and he needs to do that straight away," he said.

Latest News from Sports News Desk