Di Laurentiis, a prominent Italian film producer, publicly criticised both Sarri and the team, imposing a media blackout on them after they went down 3-1 in the away leg of the round of 16 tie.
Italian media said the comments worsened a relationship already put under strain by criticism from Di Laurentiis following a draw against Palermo in January.
Sarri, who has turned Napoli into a free-scoring side and arguably the most entertaining in Serie A, said the two men shared the objective of overturning the deficit on Tuesday.
"We were united by necessity, now the common aim is to do well," Sarri - forced to give a press conference under UEFA rules - told reporters on Monday.
"...In nearly half an hour, we talked about cinema for 28 minutes and football for 30 seconds, but only in general about future situations."
Sarri acknowledged that Napoli, who have never reached the quarter-finals in Europe's top club competition, faced a huge task, even with an away goal in the bag.
"It appears impossible for us but we must try to make their life difficult," he said.
"The most important aspect is in defence... We must avoid losing the ball near at the back. We need to keep them at bay for as long as possible."
He warned his team they could not afford a single lapse in concentration, pointing to Saturday's 2-1 win at AS Roma when Napoli dominated the match but still had to cling on at the end.
"We did really well for 86 minutes, then panicked for the last four and stoppage time," he said.
(Writing by Brian Homewood in Berne; editing by John Stonestreet)
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