The Tykes' draw at Leicester on Saturday stretched their winless run to 10 league matches to keep them in the bottom three.
But Dawson insists they must quickly switch focus to next weekend's crucial Yorkshire derby against fellow strugglers Sheffield Wednesday.
"We've stuck together and we believe in what we're trying to do," he told the club's official website.
"It's three points up for grabs, no matter what team you're playing.
"Every game is massive for us. Hopefully we can turn things around and start to push up this league."