Last season was United's worst in the Premier League, finishing sixth with 58 points, their lowest tally since the top flight was revamped from the old First Division in 1992-93.
Sheringham questioned the appointment of former Ajax head coach Ten Hag, saying the fallen giants need a boss with Premier League experience.
And the former United striker worries the club could fall even further behind rivals Manchester City and Liverpool while Ten Hag tries to adapt to the league's unique challenges.
Sheringham, right, said: "I don't know an awful lot about Ten Hag, but he's got a tough job on his hands.
"The scale of the job at United is huge and I felt they needed someone who knows and has experience of the Premier League.
"Ten Hag will not know all his players inside out yet. He doesn't know how fast it's going to be or the intensity of the league.
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