Derby claimed on Friday that a man caught acting "suspiciously" near their training ground a day previously was a Leeds employee, an incident that will be investigated by the Football Association.
Police confirmed a man was found and questioned at the perimeter fence of the complex, before being sent on his way with no arrest made.
Leeds boss Bielsa accepted in a pre-match interview before Friday's 2-0 win over the Rams that he was personally responsible for sending a club employee but showed little remorse in defending his actions.
He told Sky Sports : "Yesterday I talked to Frank Lampard and he told me I didn't respect the fair play rules. I have a different point of view but the important thing is what Frank Lampard and Derby County think.
"I didn't ask permission from Leeds United to do it so it's my responsibility. Without trying to find a justification, I've been using this kind of practice since the qualifications for the World Cup with Argentina.
"It is not illegal, we have been doing it publicly and we talk about it in the press. For some people, it's the wrong thing to do and for other people, it's not the wrong thing to do."
The Championship leaders have now stated their intention to speak with Bielsa, who conceded he personally sent the man in question without notifying the club, regarding his remarks.
A club statement read: "Following comments made by Marcelo Bielsa yesterday the club will look to work with our head coach and his staff to remind them of the integrity and honesty which are the foundations that Leeds United is built on.
"Our owner Andrea Radrizzani has met with Derby County’s owner Mel Morris to formally apologise for Marcelo's actions.
"We will make no further comment on this matter."
The issue has received widespread condemnation, with former Newcastle United and Tottenham midfielder Jermaine Jenas – now a prominent pundit – calling for Leeds to be hit with a points deduction, while Keith Andrew labelled the incident "disgusting".