McPake chose to keep his counsel regarding the Scottish Football Association's notice of complaint handed to the striker on Wednesday for three alleged rule breaches relating to last week's flashpoint in which the striker allegedly kicked a smoke bomb in the direction of a stand housing St Johnstone supporters.
He said: "It's an ongoing investigation. There isn't much I can say."
A hearing has been set for October 14. Griffiths was also charged by Police Scotland over the incident last week.
As things stand, he will be available for this weekend's rematch with St Johnstone at McDiarmid Park if he can shake off the ankle problem that forced him off in the first half against Rangers last weekend.
Asked if the uncertainty surrounding Griffiths' longer-term availability was a distraction, McPake said: "It's the process. We've been here before. I've been in the game a long time. That's the way football works. Leigh can play through it. We'll use him until we know if there is a ban.
"He's struggling with his ankle and we'll assess it as the week goes on. He's played in big games and he's been in situations before so I don't think this is anything new to Leigh. It's just something we need to deal with as a football club.
"He's come out and apologised and from the conversations I've had with him, he's OK. He's just desperate to get that ankle better."
Dundee are also awaiting the outcome of Alex Jakubiak's shoulder scan after the attacker was hurt in an altercation in the city centre last weekend.
McPake confirmed that an investigation is ongoing regarding the incident that resulted in the 25-year-old becoming injured just a matter of hours after his side's 1-0 defeat by Rangers at Dens Park.
The Dark Blues boss - who declined to discuss the events of Saturday night - said: "It's a shoulder injury. It's been scanned and we're waiting on a report."
McPake acknowledges that dealing with issues such as those involving Jakubiak and Griffiths are simply part of a football manager's remit.
He said: "It's part of the job, I know that. Certain things have popped up at different times over my two and a bit years in charge.
"We've all been in a global pandemic so there have been challenging times - not that I'm comparing the recent incidents to the pandemic because that's not right - but you're always going to face challenges as a manager and this is just another one that we need to deal with."