The current champions have won 13 league titles under manager Sir Alex Ferguson, but Gill insists that they can't rest on their laurels ahead of this campaign.
"The whole Premier League has been the greatest era for Manchester United," said Gill.
"Sir Alex has had some great teams within that. He did the treble in 1999 and won the league the next two years.
"It has been fantastic. No-one would doubt that. But you could say in 1999, Arsenal and ourselves were ahead of the other teams. Then Chelsea came along. Now we have got Manchester City. Liverpool are coming back... Tottenham.
"We have been very successful but the most important thing is that the whole club, on and off the field, cannot assume it will continue.
"We have to continue to work hard and ensure the next five years are equally successful."
United begin their title defence against West Brom at the Hawthorns on Sunday, August 14.