Scholes thinks he needs to do more on the big stage after the side could only draw at Arsenal.
He told Premier League Productions: "They (United) can't seem to win those games.
"When you're struggling against Sheffield United the other night, you're beaten by them and then you come to a big game, they just can't win them.
"They just can't find a way of doing it. Bruno Fernandes has been disappointing in every single one of them.
"He's had great numbers, great assists, great goals. In the last five games against big teams, he's had no goals, no assists.
"It's really worrying and that's why United are where they're at. They're in a good position tonight but it's not a position where you think this team will go on to win the league."