The Tigers drew 0-0 with Premier League relegation rivals Portsmouth at the KC Stadium in a dire encounter on Saturday.
David James in the Pompey goal remained a spectator for the majority and home fans voiced their disapproval towards Brown, with boos and jeers ringing around the stadium.
The Hull boss was hailed after his 2007/08 Championship play-off winners' fantastic start to last season, but they fell away from Christmas last year and continue to struggle.
Brown has therefore come under intense scrutiny, but defender Dawson is backing his boss, saying: "Phil Brown is a fantastic manager. It is doing nobody any good getting on his back.
"What the manager has done for this club is just fantastic. If we had had this start last year, we would have had a reasonable start.
"At the same time, I know how passionate these fans are and they get behind us 100 per cent of the time.
Frustration"Just like us, they get frustrated. But to go in the right direction we will have to all pull together.
"I can understand the fans' frustrations. We are all feeling it. Everybody came here expecting us to get three points judging by the reactions that I heard today. But Portsmouth aren't a bad team - let's get that straight.
"I heard a few boos at half-time as I came off and at the end you can feel their frustration at times. But everybody is giving 110 per cent.
"We are not playing the flowing football the fans want to see but everybody is trying and we need everybody behind us to get us out of the situation we are in."
Dawson also believes that the draw with Pompey was a point gained in Hull's battle to maintain their top-flight status.
"It is a clean sheet and another point on the board even though we didn't play fantastically," he added. "Getting a point is probably a game we would have lost last year.
"Fans have to learn that any point you pick up in the Premier League is a good one, no matter who it is against or where it is."