The Gills, relegated from League One last term, were in and around the play-off places for much of the season despite a slow start and even made a late push for the automatic promotion spots before ultimately having to settle for fifth place.
The Kent club lost only six matches after the turn of the year and left-back Nutter is hoping they can be rewarded for that form at Wembley.
"Especially in the second half of the season, I think we deserve to go up," he said. "I think we've been one of the best sides in the division so, if we do our jobs properly and stay focused on our game, then we've got a great chance to get back to League One.
"Nothing drastic is going to happen if we don't but obviously you want to play at the highest level. We want to play in League One and we don't just want to play there - we want to play in the Championship.
"I'm sure every footballer wants to play at the top level."