Sheringham stressed the importance of taking small, encouraging steps and allowing the manager, Ruben Amorim, sufficient time to improve the team's performance.
Manchester United concluded their worst top-flight campaign in 51 years, finishing 15th and missing out on European football after losing the Europa League final.
The former United striker warned that manager Ruben Amorim cannot afford a slow start to the upcoming season, despite retaining the hierarchy's backing.
Sheringham also commented on Rasmus Hojlund's struggles, attributing them to a lack of service rather than his ability, and noted new signing Matheus Cunha and interest in Bryan Mbeumo.