Leeds were without six first team players for their latest Premier League contest at St Mary's as Junior Firpo joined injured Kalvin Phillips, Patrick Bamford, Luke Ayling and Robin Koch on the sidelines in addition to star winger Raphinha.
The Brazilian was not risked having played 71 minutes for Brazil in the early hours of Friday morning but Cooper refused to go looking for excuses after a display in which Leeds did not manage a single shot on goal.
United's first attempt of any kind did not arrive until the 45th minute when Tyler Roberts fired over and Southampton then bagged the only goal of the game when Armando Broja finished off a counter attack that followed a Whites corner.
Asked how he assessed the afternoon's work for Leeds, Cooper admitted to LUTV: "We conceded the first half. That's as abrupt as it is.
"Not at it first half, I think we didn't win first balls, didn't win second balls and when you come to away grounds like this you are going to struggle.
"Second half I thought we played well, started the half well and then concede on the counter-attack.
"You go one behind in this league and it's always hard to come back into the game.
"But we stuck at it - I suppose that's the only positive we can take, really.
"You can't go giving first-half performances away like that and we've got to learn from it, which we do.
"Obviously we're missing a couple of players but that's just how it is, that's how it goes.
"We're back in Monday, we'll analyse it and put it right for next week."
Assessing how difficult it becomes when the likes of star men Raphinha and Phillips are missing, Cooper said: "Always. You take two of the dominant players out of any team in the league, they feel it.
"But we don't use that as an excuse, we can't use that - the lads train every single day together and whoever comes in is expected to reach those standards.
"We have belief in everybody.
"But if you lose those sorts of players, you're going to feel it a little bit."