The Uruguay striker was introduced in the final 20 minutes of Friday night's 1-1 draw against Montpellier and threatened with his first touch, a header from Javier Pastore's corner.
Cavani told L'Equipe: "I was very emotional when I came on, I heard the supporters singing my name.
"I was very motivated. It's a new adventure for me, a new phase of my life. I will give everything, like I have done in the past for every club I have played for.
"The PSG project is a great motivation and gives me great desire to win everything."
Coach Laurent Blanc said of his big-money signing: "Cavani is a goalscorer. He had a chance and it's a shame he did not score, but his introduction helped us.
"He needs game time to gel with the team. He is a player defenders will have to watch, and that will create space for others."
The reigning Ligue 1 champions trailed at half-time to Remy Cabella's goal and despite an improved second-half display and the dismissal of Montpellier's Abdelhamid El Kaoutari, Maxwell's equaliser was as much as they could muster.
"In football, the most difficult thing is scoring goals," Blanc said. "We must become more efficient or we risk having more games like this.
"We managed to equalise. We also had a lot more of the ball and more chances."
Captain Thiago Silva, though, saw the result as a positive omen.
"Last season, we also drew here before being champions," he said. "This is perhaps a wink from fate."
Montpellier coach Jean Fernandez was understandably delighted with the result.
The 2012 champions faced a daunting start to the season, with the PSG game followed by next Sunday's trip to Monaco.
Fernandez said: "It's a good result, it augurs well for the future. We have started our season well ahead of the game at Monaco.
"We played very well in the first half, with good intensity. After that, we suffered, the team had to run after the ball, tiredness set in and Paris equalised.
"I regret the dismissal of El Kaoutari but the players held on, even though it was very difficult late on."