First-half goals from Gary Alexander and Charlie MacDonald stunned the promotion favourites and gave the Bees a deserved win at St Mary's.
Adkins said: "We have lost at home again and it is not acceptable. We need to sort that out.
"We have been training really well all week but it only matters what happens on a Saturday at the end of the day.
"Their goalkeeper has made three wonderful saves in the first half.
"We conceded two goals that I am not happy about and we should have prevented them. To be honest their two strikers made it difficult for our defenders all day. They played really well."
Source: PA
Source: PA