Lampard was one of four Chelsea players fined by the Premier League club in 2001 for taking part in a drinking binge in front of American tourists in a hotel near Heathrow Airport just 24 hours after the attack on the World Trade Center.
The 36-year-old midfielder, who completed his move to the new MLS franchise on a two-year deal on Thursday, insisted he never meant to cause offence and intends to visit the National September 11 Memorial and Museum to pay his respects.
He told the Daily Mail: "I categorically did not set out to insult anyone or behave badly in front of the Americans and this is an excellent chance to say that. I'm very sensitive to the issue and the tragedy.
"I was naive and a young boy at the time. I was out on a day I shouldn't have been - I certainly wouldn't do it today. I've tried in the last 13 years at Chelsea to be not just a good footballer, but a good man off the pitch."
When asked about whether he would visit the memorial which is located where the Twin Towers stood until that fateful day in 2001, Lampard said: "It's a huge memorial and I will certainly go there to pay my respects."
Lampard left Chelsea in June following a 13-year stint with the west London club. He is the club's record goalscorer with 211 goals in his 649 appearances.