Their only Barclays Premier League victory so far has come against West Brom at Anfield, but Hodgson knows a win at Old Trafford would do wonders for morale.
However, he stressed that win, lose or draw against their arch rivals, the result will not be the pivotal moment in their season.
"You might get the shots in the arm which you help you or the kicks in the backside which bring you down, but the health of a football club should be judged by what goes on a daily basis," said the 62-year-old.
"We all know that you get your shots in the arm - like we did beating Steaua Bucharest 4-1 on Thursday in the Europa League - but we will also get our kicks in the teeth, like we did when we went to Manchester City (3-0 defeat).
"It is a part of football life and players need to be aware of that.
"If you have had the kick in the teeth, and it might be deserved, that is the reminder you have to do better.
"But when you get the shot in the arm that is the little reminder you have to be careful to keep your feet on the ground because around the corner disaster awaits.
"Having said that, we have had a really difficult start in the league and that does not get any easier, us having to go to Manchester United.
"But I see very positive signs and I'm very confident that the longer we work together, come May hopefully we will have a decent season behind us.
"This match has come a little bit early. Five games into the season is a poor time for barometer readings - they need to come at least a third of the way through the season.
"I would be very surprised if the intelligent people out there who understand the season is a marathon not a sprint will start reading too much into a defeat for one or the other teams."