The Forest player-coach saying booing from supporters it "totally counter-productive".
The Championship side crashed to a 3-0 defeat at home to Brentford on Saturday after a disastrous second half to leave them with just a single victory from their previous nine matches.
That slump has seen the club, under the interim management of Paul Williams following the sacking of Dougie Freedman last month, slip to 16th in the Championship table.
Reid, who joined Williams' staff as a coach as well as officially retaining his role as a player, said that he understands the frustrations of supporters but insisted that being vocal in their dissent will do nothing to help the team turn their fortunes around.
The 33-year-old, who has played nearly 300 times across two spells at the club, told BBC East Midlands Today: "It doesn't help anybody. We can understand the frustration, but we need them on our side.
"Fans do have the right to an opinion. Fans have always been good and very good to me, so I will never slag them off in any way, but it is totally counter-productive. We are trying to achieve the same thing, we want to win football games as much as they do.
"We urge fans, and I know it's difficult when we are not playing well, to get behind us as much as they can because we need it."
Forest's second-half collapse was greeted with dissent from the home supporters at the City Ground, who singled out Kelvin Wilson and goalkeeper Dorus De Vries for criticism after a mix-up which led to a Brentford goal, and greeted the full-time whistle with boos.
That defeat followed two relatively encouraging displays in a 1-1 away draw at promotion hopefuls Hull City and a narrow 1-0 defeat to Derby County, although any derby defeat is not likely to be taken well by supporters.
Forest face Reading away from home on Tuesday night as they attempt to get back on track.