Marco Silva’s side lost 4-0 at Crystal Palace on Sunday and now face life back in the second tier in 2017/18.
“Of course everybody, staff and players, is disappointed,” said Dawson.
“It’s been a long, hard slog and this is a sad day.
“You work hard throughout the season and then get relegated. However, we have to pick ourselves up. We know the Championship. 12 months ago we were getting promoted from it and we have to do that again next season.”
Reflecting on the performance that saw relegation confirmed, Dawson added: “We knew we had to win the game, but at half time we were 2-0 down and had to try and change it.
“Conceding the early goal meant that we were chasing the game all afternoon, and when you’re against a side that has a lot of pace on the counter-attack it’s difficult. We got caught with two late goals.
“To concede so early was a big disappointment. To go on and lose 4-0 to get relegated made it a very bad day.”