United head into this weekend 17th in the Premier League after nine matches, and with just seven points to their name.
The Red Devils are only above Crystal Palace in the relegation zone on goal difference and are also just two points above bottom-of-the-table Sunderland as pressure grows on Carrick to turn the side around.
Aston Villa's Unai Emery has already been linked with replacing Carrick, but many, such as Gerrard, believe that removing Carrick won't fix the problems at the club.
“Sometimes a performance against a certain opposition in a certain way can give the board a little bit more belief a little bit more hope,’ Gerrard said on TNT Sports.
“Michael is having a tough time, and I think the next league game is crucial. I think if he can get that win, I think everyone will think this might be the few stepping stones for them to get into better form.
“But everyone knows what a defeat (in) the last game before an international break could do. If you lose that on the back of not winning a nine in the league, I think it could be tough for him.”
He added: “I said recently that Manchester United have got numerous problems, not just one and I don’t think Michael Carrick’s the biggest problem there.”
United have won just one of their last 10 matches in all competitions, but reports suggest that a win against Villa could lift the mood at the club and potentially keep Carrick in the job after the win over Roma in midweek.
Villa are on a three-game winless run that has spanned three different competitions, giving Carrick's side a hint of confidence heading into the clash.