Stanley lost their opening Checkatrade Trophy group game, with Crewe leaving the Wham Stadium with a 3-0 win.
Callum Ainley, George Cooper and Daniel Udoh scored the goals as the visitors took the first three points in the revamped competition.
A number of Stanley players made their first starts for the club with Callam Jones, Bastien Hery and Paddy Lacey making full debuts, while new signing Rory McKeown made his bow and 17-year-old Ross Sykes made his first senior start.
As early as the first minute Crewe's Charlie Kirk curled an effort narrowly wide before Cooper drove a shot off target with Lacey responding with a strike over the bar.
Visiting goalkeeper Ben Garratt was the first to make a save, comfortably holding onto a daisy cutter from Hery and at the other end Reds captain for the night Matty Pearson blocked from Cooper in the box.
Five minutes from the break Sykes almost had his big moment, heading a Sean McConville cross narrowly over the bar.
Crewe had the ball in the net before the interval but an offside flag denied Kirk and it was 0-0 at half time.
It wasn't to stay that way, with Crewe opening the scoring two minutes into the second period. Moments after a promising Reds attack Kirk crossed and Ainley half volleyed home to make it 1-0.
Hery shot over from an Arron Davies cross as Stanley looked to restore parity and Garratt held onto a long range McConville free kick as the Reds looked to put pressure on.
Parish had to be sharp to parry from Callum Saunders to prevent Crewe putting the game to bed.
Soon the Alex did have their second goal, with the ball looping up inside the Stanley half and allowing George Cooper to outpace the defence and stroke an effort past Parish from inside the box.
Garratt was called into action as Stanley looked to set up a nervy finish for the visitors - he pushed out a fierce half volley from John O'Sullivan after the Irishman had met sub Luke Wall's cross - but the keeper's goal remained unbreached.
Instead Crewe added a third in stoppage time, with sub Udoh meeting a left wing cross at the near post to make it 3-0.
Stanley: Parish, Jones, Sykes, Pearson, McKeown, O'Sullivan, Lacey, Davies, McConville, Hery, Kee