The Whites suffered a fourth Premier League defeat of the season at St Mary's Stadium, going down one-nil.
Cooper admitted the performance was not good enough and the side will have to improve ahead of next week's home match with Wolverhampton Wanderers.
“We conceded the first half, that's as abrupt as it is," said Cooper.
“We weren't at it in the first half, we didn't win first balls, we didn't win second balls and when you come to away grounds like this, you are going to struggle.
“We started the second half well and then conceded on the counter-attack.
“When you go behind in this league, it's always hard to come back into the game, we stuck at it and that is the only positive we can take really.
“You can't give first half performances like that and we have to learn from it.
“We've got to put it right and if there is any team in the league that is going to analyse it and put it right, it is us.
“We will train hard next week to try and get the result."
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