Lionel Messi put Barca ahead with a 27th-minute penalty, before a Kylian Mbappe hat-trick and Moise Kean goal put PSG in a commanding lead going into the last-16 second leg clash in three weeks' time.
It is not the first time Barcelona have been outplayed on Europe's biggest stage as they suffered a humiliating 8-2 Champions League quarter-final defeat to Bayern Munich last season.
But anger from Barcelona fans would have intensified when seeing their manager, Koeman, laughing with PSG midfielder Gueye at full-time on Tuesday night.
The Dutchman worked with the 31-year-old for more than a year at Everton after signing him from Aston Villa in 2016.
And despite the damaging result to Barcelona's chances of progressing to the Champions League quarter-finals, Koeman appeared to enjoy his brief reunion with Gueye, who was taken off at half-time by PSG boss Mauricio Pochettino.
Koeman, who replaced Quique Setien in the Barcelona dugout last summer, is under pressure with his side eight points off LaLiga leaders Atletico Madrid.
And PSG's ruthlessness at the Camp Nou will only increase the question marks surrounding his Barcelona future.
Barcelona boss Ronald Koeman was spotted laughing with Paris Saint-Germain star Idrissa Gueye after his side were thrashed 4-1 at home in the Champions League.
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