Scott Burton was given his marching orders five minutes into the second period when the score was still 0-0.
Altrincham made the most of their advantage, scoring four goals and taking all three points to pull four clear of the Blues.
After the game, Morley said the way his side reacted to the sending off worked in Altrincham's favour.
"This is a side he’s (Phil Parkinson) had for 18-months," he told the club's video service.
"They understand each other’s strengths and they’re a great passing side. But what they’re good at, we stopped them doing it in the first-half.
"We’ve actually gifted them the game in the second-half by going down to ten men - we don’t help ourselves.
"People will question whether we can manage against ten men. It’s having the players to be able to do that and we clearly don’t have the players. We just don’t seem to have that mentality, but it takes time to install into them. But firstly, we have to stop going down to ten men. For me, it’s been far too often."
Chester's form on the road has also been an issue this season. Only Nuneaton Borough have been worse on their travels than Morley's side.
"I don’t like to be labelled a side that can only win at home.
"I do feel like we can do this as a team but we’re running out of time and we’re running out of excuses."