Andre Villas-Boas took aim at Thomas Tuchel and poked fun at Paris Saint-Germain's Champions League failure after Marseille's win.
Florian Thauvin's first-half goal was enough for Marseille to end a 20-game winless run against PSG in a fiery Le Classique in Paris on Sunday.
Five players, including PSG star Neymar, were sent off in additional time at the Parc des Princes.
Marseille head coach Villas-Boas said he exchanged words with PSG boss Tuchel, who has overseen back-to-back losses to begin the 2020-21 Ligue 1 season.
"Normal insults – you're a s***, no, you are a s*** yourself," Villas-Boas told a news conference.
"He told me I played lottery tonight, I told him he played lottery too against Atalanta [in last season's Champions League quarter-finals].
"Fair enough. I have a huge respect for him, I appreciate what he does."
PSG needed two late goals to beat Atalanta in August before they fell to Bayern Munich in the decider.
Villas-Boas said the pressure was on Tuchel to deliver a Champions League title to PSG.
"Obviously PSG wait for a cup, the Champions League, you can't invest $1.5billion and not win the Champions League," he said.
"[Carlo] Ancelotti was here, now he is coaching Everton. [Unai] Emery was here, now he is coaching Villarreal. It's hard. They wait [for] the Champions League.
"I appreciate him. They play well, defend well and aggressively. I told him: 'Unfortunately I can't play like you.'
"But I really like him."
PSG approach Wednesday's match with Metz pointless after two Ligue 1 matches and still seeking their first goal of the season. The last time the club was in such a position was the 1978-79 season.
Marseille, who face Saint-Etienne on Thursday, have won both their fixtures ahead of their curtain raiser at Stade Velodrome.