PSG took a huge step towards the Champions League quarter-finals with an emphatic victory in the first leg of their last-16 tie.
Cavani, celebrating his 30th birthday rounded off the scoring after a double from Di Maria sandwiched a goal from Julian Draxler.
The Uruguay international enjoyed the occasion, but was quick to point out that PSG cannot lose focus on domestic matters.
"For four seasons I have been in Paris and we have played some great matches, but this victory has a rather special flavour because of the meaning of this day for me," Cavani told beIN Sports.
"We are all very happy. We have done a great job but tomorrow we will have to recover.
"For now, we are not thinking about the second leg. We must focus on the league and the domestic cups, which are also very important.
"It will be necessary to prepare for the match in Barcelona because football is beautiful because you never know what can happen before a game."
Di Maria, who turned 29, opened the scoring with a fine free-kick before striking again in the second half, and was also delighted with what he saw.
"We could not imagine a better night," said Di Maria, as quoted by UEFA.com, having celebrated his 29th birthday in unforgettable fashion.
"Winning 4-0 against Barcelona on my birthday is incredible. It was the perfect match.
"To win, it was necessary to make a match like today. But we know they too can score four goals."