Dawson was taking charge of the Tigers for the first time after Tim Walter's dismissal in midweek, but couldn't prevent City from slumping to another loss, with Tommy Conway hitting a double and the in-form Finn Azaz also on target for Boro.
Hull are now winless in ten games in the Championship and, following last season's seventh-place finish, are stuck in the relegation zone.
"It's difficult because emotion always run deep when you're on the run that we're on," said Dawson.
"We've lost another game. I feel the pain and all the staff do, we're feeling it, of course we are.
"When I take myself away from the disappointment and ask did they do what we asked of them? Yes, they did.
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