The Football Association has vowed to investigate after Leeds boss Marcelo Bielsa admitted "full responsibility" for the spying incident at Derby's training ground.
The Rams' trip to Elland Road to face the Sky Bet Championship leaders on Friday night was overshadowed after a man was caught outside Derby's training ground on Thursday.
Derbyshire Police were forced to intervene and it was alleged that the man was an employee of Leeds who was spying on their opponents' preparations.
After speaking to Bielsa over the phone, and the Argentinian admitting it in an interview prior to the game, Lampard suggested Derby would not be making a complaint and would leave the matter in the hands of the authorities.
Shortly after an FA spokesperson announced: "We are aware of the incident at Derby County's training ground and we will be investigating the matter."
Asked by Sky Sports if he would be making a complaint, Lampard said: "I don't think we need to, because he's admitted it so it's easily dealt with.
"We had somebody the day before our first game against them which we lost 4-1. Now Leeds can beat you 4-1, they're a fantastic team, but we had somebody in the bushes that day, twice this season now..."
Bielsa had earlier admitted it was something he had done previously but Lampard was not interested in discussing any potential cultural differences which might see such incidents become more frequent in this country.
The former England midfielder said: "I don't care if it's cultural. Because if it's cultural and it happens in another country, if I'm lucky enough to do well and a possibility comes up later in my managerial career, when I travel to that country I will find out what the etiquette is - and I will abide by it."
The EFL had earlier released a statement suggesting it was still awaiting an official complaint from Derby, but Bielsa's pre-match comments could see its stance revisited after he admitted to sending someone to the Moor Farm complex.
The Leeds boss said: "It's true there was someone from Leeds United, the responsibility of this is (down to) me, I am responsible.
"It doesn't matter if this is legal, illegal, right or wrong. For me it's enough that Frank Lampard and Derby County felt it was not the right thing to do. I didn't behave well.
"Yesterday I talked to Frank Lampard and he told me I didn't respect fair play. I have a different point of view on it but the important thing is what Frank and Derby think.
"I am responsible for it because I didn't ask Leeds United for permission to do it. Without trying to find a justification, I have been using this kind of practice since qualification for the World Cup with Argentina.
"This is not illegal, we have been doing it publicly, we talk about it in the press - for some people it is the wrong thing, for others it's not."
An EFL spokesperson earlier said: "We are aware of the reports in relation to an incident at the training ground of Derby County.
"It is, of course, up to Derby County as to how they progress this matter but as of yet we have received no complaint or contact from the club."