Wrexham’s sole competitive victory since gaining promotion from League One came against Hull City in the first round of the EFL Cup – with Parkinson’s men beating the Tigers on penalties following a thrilling 3-3 draw in regular time.
They face unbeaten Preston North End in the second round at Deepdale on Tuesday night (19:45 BST) but will be without summer signings Liberato Cacace and Nathan Broadhead – although striker Kieffer Moore will be assessed before the contest with Paul Heckingbottom’s side.
“Libby {Cacace] is on the grass today but tomorrow will come too soon for him,” said Parkinson.
“Kieffer, his ankle has settled down again so we’ll look at him tomorrow.
“Nathan Broadhead’s got a bit of a tight calf and we have to be cautious with players because the ones who have come in and been at other clubs have picked up little niggles, some worse than others with George [Thomason] and Josh [Windass], so we’ve got to be careful with Nathan, but he’ll get there.”