The visitors were under the cosh for much of the first half at the Liberty Stadium, but the dismissal of Wilfried Bony prior to the break helped turn Saturday's game in their favour.
Southampton piled on the pressure, seeking a third consecutive league victory, and were eventually rewarded when Victor Wanyama fired the winner 10 minutes from time.
Wanyama's first goal for the club wrapped up three points to send Southampton second behind Chelsea - although Koeman is eager to remain focused.
"It's nice for the fans and everyone who loves the [club] but as a manager, and as technical staff, we have to keep quiet and continue what we are doing," he told reporters.
"There is no time to celebrate or watch the table too much. Football changes very fast and you have to prepare yourself that way.
"It was a different win; a tough one, a difficult one against a strong Swansea.
"After the [sending-off], it changed. Always those kinds of decisions of the referee are difficult for one [team] and better for another.
"We had the patience to wait, create the positions and score a great goal.
"I said at half-time: 'the worst result is 0-0, wait for the moment and be patient for the real good moments to create'. We didn't do it often but once or twice was enough."
Following Wanyama's first Southampton goal since arriving in July last year, Koeman was delighted to see the Kenya international get the winner, hailing the contributions made by his midfielders in recent weeks with Morgan Schneiderlin counting three goals to his name this term.
"[It was] a great goal, [Wanyama] gave spirit to the team when he came in," Koeman continued.
"You need players who can score - not only the forwards but the midfield players.
"The midfielders are doing well, it's always a difficult decision which three we will play but if they score, like Morgan did last week, it's great and very good for the team."