Stanley boss John Coleman was frustrated after his side lost their 10 year league unbeaten league record against Morecambe.
An Aaron Widlig goal in the 13th minute separated the sides and Alan Goodall also hit the post for the Shrimps.
But Stanley missed a number of chances with Adam Morgan and Josh Windass failing to make the most of their opportunities.
"I have to congratulate them as they have laid their ghost to rest," said Coleman. "We have played a lot better Morecambe teams than that and not lost so we are disappointed.
"Even the staunchest Morecambe fan would agree that they were outclasssed in the first half but they scored the goal and it was bad defending on our part.
"You can't miss the chances we did in games but fate conspired against us as it has in the first three games. We have got to get a win soon or we will get in a rut."