The centre-half was slated for his performance in his country’s 7-1 semi-final defeat to Germany and, although he feels that the criticism he received was unwarranted, the 27-year-old says it is now time to move on.
"I've had time to digest the end of our World Cup and now I'm ready to do everything to help PSG,” Luiz stated at his official unveiling on Thursday.
"If the World Cup had finished at the quarter-final stage then you wouldn't be asking questions about my ability.
“But I feel privileged. I'm now part of a fantastic team in which everyone has something to teach me. It's wonderful to be part of this project.
"I am very happy to have joined a big club and I'm just eager to start playing."
Luiz's £40million move from Chelsea to PSG means he will now be able to play alongside his central-defensive partner for Brazil, Thiago Silva, on a weekly basis.
The 27-year-old freely admits that he is delighted at having been reunited with his Selecao team-mate but insists that he is also willing to play in midfield for coach Laurent Blanc.
"Thiago Silva and I are very good friends," Luiz enthused. "We understand what the other is thinking with one look and we respect each other.
“We trust each other and will give our all out on the pitch. But I am ready to help out in any position, it's not up to me to choose, I just play football."
And PSG president Nasser Al-Khelaifi hopes that Luiz can inspire the club to a first Champions League triumph.
"I am very happy with his arrival," the Qatari stated. "I hired him for his many qualities, both as a man and as a footballer. David has an excellent team spirit and many other great qualities.
"David Luiz will help us achieve our goal of winning the Champions League."
PSG begin their Ligue 1 title defence against Reims on Friday at the Stade Auguste Delaune.