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."
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.