The Brewers bagged all three points thanks to a late free-kick from Jacques Maghoma. But Rowett was full of praise for the Shrimpers, who had midfielder John Spicer sent off after just 13 minutes.
"Southend were absolutely terrific and a draw was the least they deserved, but you could argue we got our rewards for carrying on and pushing for the goal," said Rowett.
"That is probably the worst we have played and we still managed to come away with three points so we have to be pleased.
"It was an excellent free-kick from Jacques at the end but I didn't want him to take it at first as I thought it was too far out. He has now scored two free-kicks for us this season and has probably never scored one in training in the three years he has been with us.
"A win in League Two is never easy to come by and funnily enough before the game I was saying we have had no luck this season. I wasn't trying to curse anyone but we managed to get that bit of luck."