The Red Devils ended 2017-18 trophiless in a campaign that will best be remembered for finishing 19 points adrift of their rivals in the Premier League runners-up spot.
Sheringham, who famously lifted the treble during his time at Old Trafford in 1999, expects a vast improvement from United's players in Jose Mourinho's third term in charge.
"Manchester United are all about winning stuff and they haven't done that [this season]," he told Sky Sports News. "It's very unusual for Jose Mourinho as well because he knows how to win trophies but, they'll have to do better next season.
"There's a lot of Manchester United players that are not playing to their full potential, that's up to them and to the manager to sort that out.
"Man City have taken the game to a different level this year and they will probably be doing it again next season, so they'll have to get a lot better."