The Magpies have lost five league games in a row and are only four points above the relegation zone.
Crossley told BBC Radio Nottingham: "If Notts County were without a manager and looking for someone to get them out of it, John would be an automatic choice."
Sheridan, 52, and Crossley, 47, joined Notts prior to the start of the season.
"I know the chairman is really eager for us to do well," added former Nottingham Forest keeper Crossley.
"He has been brilliant with and he still thinks we are the right people to turn it around. We can ask no more from him. He is with us and by us.
"But we're realistic. We have lost five on the bounce and this is a results-based industry.
"We know what we have to do and as far as we are concerned we will do it. But we need more from the players."
Crossley said the club had "targets" and were looking to bring in players in the January transfer window as they look to get through a "sticky period".
"Things have to change. We realise that and they will change in January," he said.
"There is only way to get through this and that is by everyone working hard every single day and eventually it will turn."

Offences for which lower compensation was awarded included ones involving drink, drugs or violence.
The Criminal Injuries Compensation Authority said statutory guidance obliged it to reduce or refuse awards if victims had unspent convictions.
A leading child abuse lawyer called for a review of the "scandalous" approach.
Alan Collins said civil case judges increasingly took the opposite view, and accepted that abuse could have a lifelong effect, with addictions being a possible consequence.
Since 2010, CICA - an executive agency sponsored by the Ministry of Justice - has awarded compensation to 12,665 people who were sexually abused as children, or as adults lacking mental capacity.
But some 438 people have had their government-funded compensation reduced because they had committed criminal offences themselves, the BBC learned after a series of Freedom of Information requests.
Of the 27 cases where compensation was reduced between June 2014 and June 2015, half were for drink, drugs, theft or property offences. Eight involved violence against people.
CICA would not say how many applications by such victims had been rejected.
"The Criminal Injuries Compensation Scheme has always asked that awards are reduced or refused if the victim had unspent convictions," it said in a statement.
The Ministry of Justice said the refusal or reduction of an awarded payment reflected the fact the individual "may have caused distress, loss or injury to another person, and cost the taxpayer money through a police investigation or court proceedings".
It said there were no plans to review the scheme.
Odette Tovey, a Sheffield-based legal representative for several grooming victims whose applications have been rejected by CICA, said: "The crimes committed against the victims far outweigh the crimes that these victims committed."
Some of these had been abused for many years, from their early teens, added Ms Tovey, and CICA was their only route to potential compensation.
Ms Tovey said CICA needed to take into consideration that victims' crimes "were as a result of mental health problems developed because of the period of abuse they went through".
Victims could be eligible for compensation of Â£27,000 if no deductions were made, said Ms Tovey.
The average award after CICA compensation reduction was Â£8,423.
Jane was groomed and abused for more than four years after running away from her South Yorkshire home at the age of 15.
She was given drugs and alcohol and forced to have sex with men she did not know.
A lead witness at her abuser's trial, Jane was turned down for compensation because she has unspent convictions for theft and assault - offences which took place before the trial took place and when she says she was addicted to so-called legal highs.
She has since given up drugs, has married, and is pregnant with her first child.
Jane - not her real name - has paid back the money she stole and says she feels remorse for her actions, but says they should not negate her compensation.
She told the BBC: "I've hurt someone else, they didn't expect to be hurt, they didn't deserve to be hurt, I just hurt them so I could get money.
"I've been told by a couple of people that they received about Â£15,000, and that makes me really angry - because while the main witnesses haven't received anything, the others have."
Assistant manager Mark Crossley says boss John Sheridan has the backing of chairman Ray Trew, despite Notts County slipping to 20th place in League Two.
[NEXT_CONCEPT]
Compensation has been reduced for more than 400 sex abuse victims in Britain who later committed criminal offences, the BBC has learnt.