The Red Devils were held to a 1-1 draw by FC Twente on Wednesday night in the Europa League.
United have won three of their opening seven matches of the season, with victories against Fulham and Southampton in the Premier League as well as a crushing win against Barnsley in the Carabao Cup.
Hargreaves expressed his concern over a United side who are yet to beat a big team.
“That's the biggest issue so far this season, they haven't really beaten anybody.
“There was the Liverpool game (a 3-0 defeat). Against Crystal Palace (a 0-0 draw on Saturday) they probably should've won. The first half was exceptional, but then in the end, if it wasn't for an (Andre) Onana double save, they could have lost that as well.
“This will be a bit of a blow because the season has gone a bit like this – they had control of the game but couldn't finish it off.
“I think that allows a team like Twente to grow in confidence, be positive, and in the end they leave Old Trafford with a point. They pushed, they went for it and got what they deserved.”
He added, “When you play for a team like Man United you need to rise to the occasion.
“They have done it in some one-off games when they have been up against it, but they are going to be tested in their next seven games. They need to find solutions. Erik sticks his neck out every time and he is honest.
“But the fact of the matter is they need results, that is all this business comes down to when you are a top team, getting results.”