The influential pair were in discussions to remain at Hillsborough, but have elected to exercise their right to leave under freedom of contract at the end of this month.
It is a blow for Monk and the Owls, who are sweating over the outcome of an EFL misconduct charge which could see them be handed a hefty points deduction and be plunged into a Championship fight if they lose their case.
On exits of key defender Fox and top-scorer Fletcher, Monk: "All of us would have preferred this to finish in a normal way, but we are not in normal circumstances.
"The most important bit is we have to accept the players' decisions whether to extend, not accept or agree on a contract that has been offered.
"Obviously, with Foxy and Fletch, we have not been able to come to an agreement in terms of contract and I think the right thing to do is pay respects to them and wish them all the best for the future and thanking them for the service they have done
"What I have to do now is focus on the players that are here and committed to finishing these games and beyond.
"The best way to handle that is to accept their decisions and then to try and move on and wish them all the best."
Monk also insists he is not expending any energy worrying about the club's legal fight with the EFL over charges of breaching Profitability & Sustainability rules - and is focusing on controlling what he can control in terms of playing matters.
The Owls' case is being heard by an independent disciplinary commission after the dispute was brought forward following complaints from a number of rival clubs, including Barnsley.
He commented: "My job is to control the football side of it. I have spoken to the club many times and the club are confident in terms of their side of it and we just have to get on with our jobs.
"I cannot waste energy worrying about that. Our job is to focus on these games and try and perform and get as many points as we can regardless. Of course, we will see how that plays out, but of course, we will see how that plays out.
"But the club feel confident; they always have done all the way through. Whenever that goes and what it looks like, we will deal with that at that time."
Meanwhile, Monk has confirmed that the club are awaiting paperwork regarding loan extensions for Jacob Murphy, Josh Windass, Conor Wickham and Alessio da Cruz, with the Owls chief confident that they will be at the club for the remainder of 2019-20.
Windass is currently sidelined with a thigh issue, but Monk is hopeful he will be back in consideration in a week to ten days.
Monk added: "As it stands, it should just be a matter of paperwork now with those guys.
"So we are very pleased with that. Once we spoke a couple of weeks ago about that side if it, straightaway we wanted to commit to it and see the season off.
"Other clubs have all agreed and it is just a matter of paperwork as it stands right now."