Louis van Gaal’s side are in fifth place in the Premier League table and 12 points behind surprise Premier League leaders Leicester City.
The Red Devils, who are in the FA Cup fifth round, also made a premature exit from the Champions League after failing to qualify for the last-16.
Van Gaal is facing an uncertain summer, with former Chelsea and Real Madrid manager Jose Mourinho being linked with a move to United.
Irrespective of whether the Dutchman is still at Old Trafford, Cole warned United that they can ill-afford another disappointing campaign with Pep Guardiola set to take over the reins at Manchester City.
“United need a good side next season,” Cole told Yahoo Sport. “My loyalty is with the Reds and we can’t have another year of being so far from the top, especially with City likely to be stronger with Guardiola.”
Van Gaal has failed to win any silverware since the former Barcelona and Bayern Munich manager was named as David Moyes’s successor in 2014.
United make the trip to Sunderland in the Premier League on Saturday.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news