Koch was left covered in blood after a clash with Scott McTominay early in the match but returned to the pitch with his head bandaged before going down again and finally being taken off.
Football Association guidelines state that any player that sustains a suspected concussion should immediately be removed from the pitch, and extra permanent substitutions are allowed in such cases.
But the PFA believes temporary substitutions to allow players to be fully evaluated before a decision is made about them returning to play are needed.
The organisation said in a statement on Twitter: “The injury to Leeds United’s Robin Koch demonstrates again that the current concussion protocols within football are failing to prioritise player safety.
“The ‘if in doubt, sit them out’ protocol is not being applied consistently within the pressurised environment of elite competitive football.
“We see frequent incidents of players returning to play with a potential brain injury, only to be removed shortly afterwards once symptoms visibly worsen.
“As the representative voice of players in England, we have been clear to @TheIFAB that we want to see the introduction of temporary concussion substitutes.
“Temporary concussion substitutes will allow medical teams additional time and an appropriate environment to make an initial assessment.
“Introducing temporary substitutes would allow a match to restart with neither side numerically disadvantaged, reducing pressure on players and medical teams to make quick decisions on whether an injured player continues.
“Put simply, the current rules set by @TheIFAB are not working, and players are being put at risk.”
Speaking about the incident after the match, Leeds boss Marcelo Bielsa insisted the cut rather than the force of the blow to Koch’s head was the reason for his withdrawal.
“He had a cut in his head and what excludes him or made him come off is the cut,” said the Argentinian.
The decision not to substitute Koch immediately drew criticism from several quarters, though.
John Stiles former Leeds and Doncaster Rovers and son of England and Manchester United legend Nobby Stiles tweeted: ‘How on earth could they leave the Leeds player on after that head injury -does a player have to die before they act?’
Pundit Chris Sutton, whose father Mike - a former professional footballer - died from dementia in 2020, wrote on Twitter: “Football doesn’t care about its players. What needs to happen before the concussion procedure changes?”