Ghana's coach Kwesi Appiah introduction of two strikers Patrick Twumasi and Dwamena was not enough to fetch the desperate Stars the needed victory to keep their world cup dreams on hold.
The Ghana federation says it wants FIFA to "examine" the performances of Bennett and his assistant referees in its match.
In a controversial contest, Ghana had a goal disallowed at the death with the linesman wrongly flagging Raphael Dwamena offside, despite replays showing the Black Stars forward was comfortably onside.
Last month Federation Internationale de Football Association also ordered for a replay of a 2018 World Cup qualifier between South Africa and Senegal after it was discovered that the referee handled the match poorly.
"We have to protest. this no "fa ma Nyame" matter. i'm so furious", Gyan tweeted after the game.
"Referee Daniel Bennett just told the Ghana team why he disallowed the goal".
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Yesterday's crucial game between Ghana and Uganda in the World Cup Qualifiers was full of big events.
With that number, with one party remaining, Egypt has been confirmed to be the group victor and secure a ticket to the 2018 World Cup finals.
The result leaves Ghana at third in the Group E with six points behind leaders Egypt and Uganda.
"Mr Bennett and assistants denied Ghana a ideal goal in the 93rd minute with television replays showing that it was a flawless goal".
First of all, a clear penalty in the early stages of the second half was not awarded after Frank Acheampong was impeded in the box by rushing Cranes defender.