Forest will get the new Championship campaign underway at home to newly-promoted Millwall on Friday night as Warburton prepares for his first full season in charge at the City Ground.
The club only narrowly avoided relegation last season, but Warburton is confident that they have the ability to push for promotion to the top flight after 18 years away.
"There has to be a togetherness. It is a statement used too often, but it is all about the unity and the harmony displayed by the players, the staff, the fans and by the whole club," he told the club's official website.
"It is not just at the training ground or just at the City Ground, it is about one club together and if you can get it right, the results can be quite spectacular."
Forest finished 21st in the Championship last season, only beating the drop on goal difference.