Rickie Lambert took his tally for the season to 18 in the 26th minute when he headed home Ryan Dickson`s teasing cross.
And Lee Barnard secured the points when he tapped in a cross from strike-partner Lambert three minutes before full-time.
Yet Dawson said: "It was a disappointing result but we have not given up hope of getting in to one of the promotion play-off places.
"Some results went our way and we have to keep on believing that we can make the play-offs. Southampton proved themselves a good side and after this result I am convinced they will go up.
"I know we had a couple of goals ruled out for offside but I am not complaining about them. I have seen them on the monitor and as far as I am concerned both decisions were spot on."
Source: PA
Source: PA