Nade was allegedly the aggressor in his fracas with playmaker Black in the wake of Wednesday's 2-0 loss at Celtic.
Jefferies, though, insisted Nade was omitted from Saturday's squad due to recent poor performances and not the behind-the-scenes issue.
Black started the match and notched the decisive third goal with a superb left-footed strike from long range.
Asked if Nade will play again for the club, Jefferies said: "We will wait and see what the outcome of the discipline is, it's too early to make any decisions on anyone.
"The club have made a statement that we will deal with that internally and I can't tell you what it will be.
"In general, if they don't perform and play then that can apply to someone else that might not play for Hearts again because they are not doing well enough.
"They have all got a chance, everyone knows I'm hard but fair."
Jefferies, who revealed "slight" progress had been made over contract talks with defender Jose Goncalves, added: "I left him (Nade) out, maybe a little bit of that (the incident) but mostly because I don't think he has been doing well and I don't think he has been scoring goals.
"We left him out and put (David) Obua up there with young Gary Glen and we have scored three goals and I have been justified.
"We didn't leave him out for disciplinary reasons, I left him out because I would not have played him anyway."
In Jefferies' return to the home dugout at Tynecastle nearly 10 years after ending his first managerial stint in Gorgie, Hearts picked up their first win under the former club captain at the fourth attempt.
Lee Wallace opened the scoring after five minutes when his cross caught out Robert Olejnik as it sailed into the net at the near post.
Hearts defender Dawid Kucharski brought Falkirk level with an own goal in first-half injury time.
Suso Santana and Black struck after the break, although Hearts endured a tense finish when Falkirk substitute Pedro Moutinho scored seven minutes from time.
New Falkirk manager Steven Pressley, in his first game since taking over the reins from Eddie May, felt his team did not deserve to lose.
The former Hearts captain, who made a bold move at the interval when he brought on striker Enoch Showunmi for winger Jack Compton, said: "I spoke to the players about two key ingredients to our survival and that is spirit and desire, and I saw plenty of that.
"We had enough to come from 1-0 down and I thought we had the best of the second half. We found ourselves 3-1 down but we showed terrific character.
"I know we lost the game but in my opinion I thought we didn't deserve to do so."
Source: Team Talk