Parkinson admits Wright's injury 'doesn't look good' after the defender hobbled off with an ankle problem.
Ozturk was summoned from the bench to replace Wright in the final stages of the second half at the Kassam Stadium.
On Wright, Parkinson said: "It doesn't look good, that's all I can say at the moment as it is early, it looks quite a bad injury. Alim came on and did well.
The staggering average attendances for the 2021/22 season - and where Sunderland, Leeds United, Newcastle, West Ham, Liverpool and other clubs rank
Sunderland AFC transfer rumours: Rangers, Middlesbrough, QPR and Sheffield United eye £5m-rated Black Cats star - reports
Kristjaan Speakman discusses Sunderland's budget, ownership and ambitions for Championship return
Leon Dajaku becomes Sunderland's first summer signing ahead of Championship return
Sunderland AFC transfer news: Black Cats eye Premier League loan targets and prepare to open talks on Nathan Broadhead return
"It's his ankle ligaments."
Ozturk was dropped for the trip to Tranmere at the end of last month with Sunderland recording clean sheets in four out of the last five games with Wright at the back.
Parkinson admits Ozturk was ‘unlucky’ to have been taken out of the back three in order to slot January loan signing Wright in and has backed him to do the business should Wright face a spell out.
On Ozturk, Parkinson added: “Alim was unlucky to have been out of the team.
“When we made the change at Tranmere it was a tough call, if Bailey is out for a period then Alim comes in and I have no problems with that at all.
“Alim has a great personality, he is a good lad, even though he has been out of the team, he has trained well.
“We went with the same team for a period of time and sometimes it can be difficult to keep those lads going not in the team but as I keep saying in the press, they have been outstanding and have helped drive the lads in the team on.”
Sunderland have a free midweek ahead of a crunch double-header at home, with Bristol Rovers the visitors on Saturday followed by Fleetwood Town a week on Tuesday.
Sunderland stayed fifth after the victory at the Kassam Stadium but are now just three points off the top spot.
The Black Cats won 1-0 thanks to Jordan Willis' header from a Chris Maguire corner less after two minutes.