Parkinson has admitted that some players could be taken out of the firing line at Morecambe's Globe Arena due to knocks picked up during Saturday's dramatic win over Coventry City, but he insists City will still be going into the game with a strong line-up.
Some clubs have in the past been accused on taking the first round of this competition lightly but Parkinson says that certainly won't be the case for the Bantams when they take on Jim Bentley's Shrimps.
Parkinson said: "We were obviously pleased with the start on Saturday but we want to build on that now against Morecambe on Tuesday night.
"We know from our own amazing experience a couple of seasons ago that this is a tremendous competition. We want to progress in this cup and we want to put in another good performance to keep spirits high going into two tough away games in the league.
"To challenge on a number of fronts throughout the season you need some depth to you squad. To achieve that you normally need a decent cup run or a decent cup draw to help finance that."
Despite being buoyed by Saturday's tremendous Coventry victory, Parkinson knows that this Tuesday's tie won't be easy.
Opponents Morecambe, who have former Bantams loanees Jamie Devitt and Kevin Ellison in their ranks, currently sit top of League 2 after day one thanks to a fine 3-0 victory away at Dagenham & Redbridge.
Parkinson added: "We've seen them play Saturday and we've seen them play a couple of times in pre-season and all of the reports seem to suggest that they are strong team for their division this year.
"They had a great win down at Dagenham on Saturday - Dagenham is a very difficult place to go. (Morecambe manager) Jim Bentley has done a tremendous job there keeping them competitive season after season on a limited budget.
"They are always well organised and they always work hard for him.
"I have already told the lads that we must be prepared to roll our sleeves up and work really, really hard from the very first whistle. If we do that, we'll give ourselves a good chance."