Mr Barnes, 29, died in 2016 after suffering a heart attack during the restraint, where he was held down by four men - working for an external company at Manchester Victoria Station as security.
Footage taken from body cameras showed that the men chased Mr Barnes for nine minutes after an altercation. He was restrained face down and was heard saying he could not breathe seven times in the footage.
Mr Barnes suffered a heart attack, followed by a cardiac arrest and died in hospital seven weeks later.
The CPS said prosecutors are considering whether charges of assault could be brought.
But it added: “However, we are unable to reconsider manslaughter charges because there is no new medical evidence that establishes a clear link between Mr Barnes’s death and the actions of the suspects.
“We appreciate this may be difficult to understand in light of the coroner’s unlawful killing finding, but the standard of proof required for criminal proceedings is higher than that of an inquest.
"We are writing to the family to explain our reasoning and our thoughts remain with them."
Mr Barnes’ mother, Patricia Gerrard, said it felt like her son was “being let down again” and that “his life didn’t matter to others”.
Her lawyers, Hudgell Solicitors, have written to the CPS saying believe that it has made a “fundamental error in respect of causation in law and fact”.
They say if the decision is not reconsidered, the family will be supported to take legal action either by pursuing a judicial review or a private prosecution.
Mrs Gerrard said they had been overwhelmed by support from people “wanting justice for Jack”.
She said the coroner’s decision to release the footage left “no place to hide”, saying it showed “all you need to see”.
Mr Barnes repeatedly said he could not breathe as he lay on the pavement in Deansgate in the city centre after he was caught following a 1,000-metre pursuit from Victoria Station on the evening of October 11 2016.
One of the four men took over the restraint position at one point and gripped Mr Barnes' neck and held his left arm behind his back as well as putting pressure on his back.
From bodycam footage worn by a colleague he was heard to say: "We're gonna put you out pal. You're all right" and then later added: "Right, if you struggle I will put you to sleep.
"It won't kill you.
"It won't kill you, but you will go to sleep for a while."
Last month, HM Senior Coroner for Manchester, Nigel Meadows ruled the death was an unlawful killing and stated the restraint "more than minimally, trivially or negligibly contributed to the cardiac arrest."
Neil Hudgell, from Hudgell Solicitors, said: "The coroner was very clear in his findings that there had been more than sufficient evidence to conclude that Jack was killed by unlawful act manslaughter by one person or by joint enterprise.
"He added that it was apparent that the actions of the men in question constituted an assault against Jack in relation to which any sober and reasonable person would inevitably have recognised the risk of at least some harm.
"The coroner made clear that the assault and restraint was plainly an operative cause of death and consequently we have written to the CPS to say we strongly believe that it has made a fundamental error in respect of causation in law and fact.
"We have asked them to reconsider their position on the understanding that the failure to do so will inevitably lead to our clients considering their own proceedings."
Mr Barnes had earlier taken an unknown quantity of the drug Spice before the incident when his friends had got into an argument with one of the staff about allegedly consuming drugs on the trams and platforms.
It led to Mr Barnes swinging his bag at two staff members before he was chased out of the station.