The PFA chairman believes the situation draws parity with English clubs' ban from continental competition after the Heysel incident, due to the repeat nature of the offence
Danny Rose was sent off with an ugly brawl breaking out at the final whistle after the left-back reacted angrily to alleged racist abuse from the Serbian crowd.
Nedum Onuoha was also subjected to similar abuse in a clash between the nations in 2007, which saw a £16,000 fine handed to the Serbian FA, and Carlisle has called for a much stronger punishment to be given now.
"You should not have to experience those scenes in this day and age. It was utterly deplorable behaviour," he told BBC Radio 5 Live.
"It's quite farcical. A guy is racially abused and then he gets punished for containing his reaction to that.
"We saw how the whole debacle progressed into punching, kicking... we saw photos of headbutts going on in the staff. But Danny Rose for kicking a ball away ends up getting himself sent off. This is just wrong.
"Uefa need to make a standpoint here and more importantly Fifa, I feel, because it was a Fifa qualification tournament. The message has to come from the top down that this behaviour will not be tolerated.
"It's immaterial where it is, who the perpetrators are. What's material is that the governing bodies lay down extremely harsh sanctions so that they deter countries and people from acting in this way.
"You can draw parity with what happened to English football when we were kicked out of Europe for the violence [following the 1985 Heysel disaster] - that instigated a period of self-governance.
"I believe Serbia should be banned because it's a repeat offence.
"Banning them for a start, from any tournament, would be progress but I think if it's significant - if it's a couple of tournaments - then that would cause that nation to address the issue that has deprived them of international competition."
Players have also taken to Twitter to have their say over the incident, with Phil Neville and Jason Roberts backing Rose's reaction and suggesting that players leave the pitch if they are ever subjected to abuse in the future.
Neville said: "Disgraceful what happened in Serbia last night-manager/captain should just take team off the field and refuse to play see what Uefa do then."
While Roberts tweeted: "DRose, well done! I propose next time everyone walks STRAIGHT OFF THE PITCH!!! Then we will see how quickly "authorities" take to sort it.
"I am FULLY condoning ALL Players picking up the ball and walking off the pitch..at ANY LEVEL..GAME DONE!! See how quickly things change.
"It's not about them winning its about making a proper stand-not wearing a t-shirt for 10 mins once a year-stop the game walk off shame them."
Rio Ferdinand also called for strong retribution to be handed out and criticised Uefa's previous punishments for similar incidents.
He said: "Let's see if Uefa are serious or will they just treat this U21 incident as a minor....as they have before with their laughable punishments."