Forest are one of the favourites for the Championship title after spending big during the summer transfer window, but the East Midlands outfit have only recorded one win and three draws from their opening four fixtures.
However, Dawson - who returned to the City Ground ahead of the new campaign - says that the first-team squad must stay united throughout what he expects to be a "gruelling" season.
The 34-year-old is quoted by the Nottingham Post as saying: "The teams who have come down from the Premier League always have the advantage. Of course they do, because they have been there and done it and they will have kept as many of their players as possible.
"As a Forest player, the only thing you can take care of is what happens in this club. The manager and owners are doing that and, as players, we will look to achieve things on and off the pitch.
"We have to stick together through the hard times, because the Championship is gruelling. When your backs are against the wall, you have to show a different mental strength."
Dawson has made two appearances in all competitions during the early weeks of the campaign.