Houli is expected to be taken by Richmond in the NAB AFL Pre-Season Draft, while Neagle - the son of club premiership star Merv Neagle, who played 147 games for the club and a further 56 for the Sydney Swans - has been told that if he can get his fitness levels in order, he will be offered a spot on the rookie list.
Atkinson, however, has chosen to walk away from AFL football after being told to lift his game by new coach James Hird.
Essendon football manager Paul Hamilton told Melbourne radio station SEN that Neagle, who had been seen at the club as a replacement for champion full-forward Matthew Lloyd, and Atkinson had not met the club's new training values.
"We've come back to training, and it's been very clear from James (Hird) that we have to reach certain standards," Hamilton said on Tuesday morning.
"The players need to be at certain physical standards. That's what it's been all about, making sure that as a group we improve our mental hardness and the way we go about our tasks.
"In regards to these two players, we just haven't been able to meet these standards."
Hamilton said Neagle was fortunate to have a been offered the opportunity to resuscitate his career, after just 28 games since being taken as a father-son selection with pick 39 in the 2005 NAB AFL Draft.
"In Jay's case, he's come back and certainly his testing results were well below what the required standards are.
"He's been given a lifeline in that there is a rookie spot available for him if he's able to demonstrate over the next four weeks that he's up to the training standards.
"To his credit, he was here at 7am, and out training with the guys."
Neagle has played 28 matches and kicked 41 goals since making his debut in 2007, while Atkinson appeared in 17 games in three seasons on the senior list.
