Lukas Jutkiewicz slammed home the winner for the home side - but Rovers could and should have taken at least a point as they squandered a host of chances of their own.
Colin Kazim-Richards came the closest to netting for Berg's visitors when he struck a post from close range, but ultimately it was a familiar tale of what might have been for the Norwegian.
Berg said afterwards: "We played well - maybe for spells we played better than Middlesbrough - and we created chances but we lost 1-0.
"It is very frustrating but it has been like that for eight weeks now. We are playing well but not winning games.
"In football you have to take your chances. Middlesbrough created maybe two or three and scored. We created three or four or five but we are going away with nothing.
"People talk about luck and say that we hit the post but it is time for us to create our own luck, start taking chances and start winning games."
Blackburn are now without a win in their last six games ahead of Saturday's trip to face Barnsley.