Koeman’s euphoria could be justified, however, and not just because he was celebrating his 53rd birthday 24 hours early.
Southampton had fought back from a desperate position, two down and apparently with little hope of recovery, to claim three points that could prove vital in their efforts to secure a return to the Europa League next season.
For Liverpool manager Jurgen Klopp, there were no such grounds for satisfaction.
Having seen his side take control through goals from Philippe Coutinho and Daniel Sturridge inside 22 minutes, he was forced to watch his charges collapse alarmingly after the break.
Inspired by the half-time introduction of Sadio Mane and Victor Wanyama, Southampton were as effective in the second half as they were insipid in the first.
Mane may have seen a 49th minute penalty saved, but the forward recovered to bring his side back into the game in the 64th minute before scoring the 86th minute winner after Graziano Pelle had equalised two minutes earlier.
Little wonder Koeman found himself racing to join in the celebrations. “It is the first time I have done that and I think the last time,” he said.
“I am still tired! That happened because it was a must win game for us. You need to score the first goal (after the restart) to get the feeling you can come back and get the result and that’s what makes it special and emotional.
"And of course all the goals were fantastic.”
For Koeman, this was about a Europa League spot. They now lie seventh and firmly in the mix to take their fight to the final stages of the season.
For Klopp, this result was more about drawing a line under any remaining hopes they had of reaching the Champions League although the German refused to give up the chase.
“There are 27 points still to play for,” he said.
“We can get all of them, there’s a chance. We don’t have to dream of things like this. We have to play football and win games.
"If we played like the first half we can win games. If we play like we did in the second half it will be more difficult.”
For 45 minutes it looked as though Liverpool would secure the fourth successive Premier League victory that would increase the pressure on the top four.
Coutinho exposed Southampton’s porous defences in the 17th minute, drifting in from the left before curling a long-range shot inside the far post.
Five minutes later, another Liverpool breakaway, this time led by Divock Origi ended with Sturridge placing a shot between two defenders for the second.
At that point there seemed no prospect of a comeback, although that was before Klopp decided to tweak his defence to take account of Dejan Lovren’s yellow card.
Martin Skrtel came on and was immediately caught out by Pelle, pulling the striker to the ground and was relieved when Simon Mignolet saved Mane’s spot-kick.
Mane, though, responded by easily turning Mamadou Sakho in the 64th minute and this time beating Mignolet with a left foot shot.
Liverpool missed another chance to put the game beyond Southampton when Christian Benteke fired wide when free on goal.
That would prove costly with Pelle taking advantage of the slip to level with a powerful, long-range shot six minutes from time.
Two minutes later he turned provider to tee up Mane for the late finish that sparked Koeman’s uncharacteristic reaction.
“The team performance in the second half was perfect. It wasn’t good enough in the first half but Liverpool let us in light after 45 minutes and we punished them for that and I know that feeling because we lost many games when we had to kill the game and we didn’t and now it’s different.”
Forster 6; Martina 5, Fonte 6, van Dijk 6, Bertrand 5; Davis 7, Romeu 6 (Ward-Prowse 69, 6), Clasie 5 (Wanyama 46, 8), Tadic 4 (Mane 46, 8); Pelle 9, Long 7.
Stekelenberg, Soares, Yoshida, Juanmi.
Mignolet 5 ; Flanagan 6, Lovren 5 (Skrtel 46, 3), Sakho 5, Clyne 6; Lallana 7, Can 7, Allen (Oyo 86), Coutinho 7; Origi 7, Sturridge 6 (Benteke 69, 4).
Ward, Toure, Henderson, Smith, Oyo.
R East 6