Mbappe, who missed the opening three games after contracting the coronavirus, fired PSG ahead with a 38th-minute penalty and had a big part in Angel Di Maria's strike before Marquinhos headed home the third in the second half.
"I was just happy to put the jersey back on because here in Paris when you miss a game, it's like you've missed 10," Mbappe told Canal Plus television.
"I spent the last few days watching television and I couldn't wait to come back. It was nice to score but we are still going through a complicated period and it's not easy to live with".
PSG made a sluggish start to their campaign as they lost the opening two matches and eked out a last-gasp 1-0 home win over Metz on Wednesday but they tore Nice apart with sublime skill and crisp one-touch passing.