"This squad is good enough to stay in the Premier League... It doesn't matter how we get the points on the board, we've just got to get them," Dawson told the club website (www.hullcitytigers.com).
"It's going to be a fight and there are a number of other teams in the fight but we'll keep going and keep believing."
The bottom-half of the table is tightly packed with as many as three teams leading Hull by a single point.
Middlesbrough are on 15th, ahead of Crystal Palace and West Ham United on goal difference.
"We're one point behind the teams above us at the moment, and it's a case of looking to the next game and making sure we're better than the last one," the 33-year-old said.
Hull have conceded 27 goals and lost 3-0 at the Stadium of Light last week.
"We had opportunities against Sunderland... we have to be more clinical in the final third, but we also have to start keeping clean sheets," Dawson said.
"If we had won last weekend, the table would be looking a lot different."
Hull host ninth-placed West Bromwich Albion on Saturday in their next league game.
(Reporting by Debanjan Bose in Bengaluru)
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