The Saints found themselves two goals down with around 25 minutes remaining at St Mary's but a Sadio Mane brace either side of Graziano Pelle's fabulous strike gave the home side a 3-2 win to keep their European ambitions well and truly alive.
Koeman dashed down the touchline in uncharacteristic fashion when Mane score the winner and he admits he only acted that way due to the magnitude of the victory which has the south coast club sitting seventh on the Premier League table, four points from fourth position.
"It is the first time and I think the last time, I am still tired," Koeman said.
"That happened because it was a must-win game for us today and when you are really down after half-time you need to do everything to go on and believe in yourself and score the first goal to get really feeling you can come back in the result.
"That makes it special and emotional and of course all the goals were fantastic goals. I'm proud of the team. We had a great spirit after half time and it was hard to manage it after 45 minutes.
"Normally you get this chance, they will kill you more than they did. It is fantastic, 2-0 down and the importance of the game, the support of the fans."
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