Darby missed his first game of the season on Tuesday when the Bantams played Milton Keynes Dons in the Capital One Cup due to a tight groin muscle. Despite being given the game off to rest the injury, he remains a doubt for Vale's visit to the Coral Windows Stadium this weekend.
Gary Liddle, who played at right back and captained the side at MK Dons in Darby's absence, will be in line to fill in for the Liverpudlian again should he miss out against Vale on Saturday.
Parkinson said: "He (Stephen Darby) has probably played in the past when he shouldn't have done. He is great captain and a great defender for us but we felt it was the best thing leaving him out on Tuesday because his groin was worse over time.
"Matt (Barrass, City's Head Physio) said that we needed to give Stephen a period of rest because, if not, it could turn into a longer injury for him.
"We will have a look at Darbs again at the training ground in the build up to Saturday but if he's not right, we cannot risk him.
"To be honest, we don't really need to put any risk on Stephen because of the way Gary (Liddle) played at MK Dons on Tuesday.
"It was a positive to see Gary perform so well on Tuesday because we don't have an out-and-out replacement for Darbs at right back at the moment. I was very pleased with his performance.
"Chris (Routis) has played there for Servette but I wanted to keep him and Rory (McArdle) in the middle (of defence).
"We obviously want Darbs to be back as soon as possible but it is nice to known that we have some options there now and we don't have to rush him back.
"Gary has been an important signing for us and he is a very intelligent player. His versatility is a major positive for us and I'd have no qualms about putting him in at right back again on Saturday."
Even if Darby isn't deemed fit enough for this weekend, Parkinson's defensive options for the Vale fixture will be boosted by the return of Alan Sheehan following the Irishman's recent three-match suspension for his Swindon red card.
Midfielder Matthew Dolan is also likely to be in contention once again after three weeks on the sidelines with a hip problem.