Dusan Tadic's second-half penalty was enough to secure a 1-0 victory at the Stadium of Light to maintain their bid for another lofty finish after an all too brief Europa League adventure earlier this season.
Koeman said: "I think if we reach European football, it would be like we had won the title."
Asked if that was possible, he replied: "Of course it's possible
Why not? Why not? Do you think it's possible? We have the experience from last year.
"We know it's difficult because it's not easy to beat big teams, big clubs after 38 games in the Premier League
But we have potential, we have qualities, in my opinion, we have a squad now to fight for that.
"That's very good, that's positive and we will see what happens at the end of the season."
However, Koeman admitted a top-four finish is beyond the Saints.
He said: "No, no, no
Top four? It's maybe too difficult
Qualifying for Europe means maybe seventh place - like last season - is possible, six, five, four...
"It's too early in the season to have an opinion on things about that
We like to enjoy football - that's one of the best qualities, how we like to play, and then you will win a lot of games, we know."
Southampton had the better of the 90 minutes, but were repeatedly thwarted by keeper Costel Pantilimon until Yann M'Vila's ill-judged challenge on Ryan Bertrand prompted referee Mike Jones to point to the spot and Tadic obliged to give the visitors a decisive 69th-minute lead.
Black Cats boss Sam Allardyce had no complaints about the decision, but plenty about the tackle.
He said: "He [M'Vila] didn't need to go to ground
He'd done the job, he'd covered around DeAndre [Yedlin]
Just jockey the player out of the box.
"The player sees the tackle and goes, 'That's me, I'm going down now', and he can't argue with the penalty decision because if he'd just stayed on his feet, the lad was going nowhere."
The defeat was the third in four games since Allardyce took over on Wearside, and he is desperate to rid his players of a fear factor he believes is hindering performances.
He said: "In training, I see a lot of good stuff, I see a lot of good things, but I ain't seeing it when we get on the field, that's my problem, so there's got to be a bit of fear in the players who are frightened to express themselves.
"They've got to really get rid of that fear and show on the pitch what they can do on the training ground.
"They seem to find it from somewhere at the end of the season, don't they, for some bizarre reason? The last thing I want to do is to have to try to find it at the end of the season again because you might not find it then.
"When the games go into single figures, that's it
Now we have got a lot of games to try to make sure we get out of being in that position."
Source : PA