Waldrum and the NFF failed to agree terms for the American to succeed Florence Omagbemi in the role, despite an announcement from the federation in October.
Earlier this week the 61-year-old opted to accept a new role as the head coach of the University of Pittsburgh women’s team.
“I’m quite disappointed that Randy Waldrum was appointed and he decided not to come,” NFF official Chris Green told BBC Sport on Thursday.
“I’m actually disappointed in the fact that I thought we had a good coach in him.”
“He said in his letter (to us) that from when the (NFF) president gave him the job, they did not do anything or contact him any further,” Green added.
“There are other things that are required like signing the contract itself, working conditions and all the basics that parties have to agree to – nothing was done.
“He was left in limbo and said he has to feed his family, but (we’re) extremely disappointed that we’ve lost out on another coach.”
It is the second time in 18 months that a foreign manager has rejected a coaching offer from the NFF, after Frenchman Paul Le Guen rebuffed the chance to handle the Super Eagles in July 2016.
This latest setback comes as a big blow to the Falcons, who have not played or trained since lifting the Women’s Africa Cup of Nations a year ago.