After Semi Ajayi was sent off just 30 minutes into the match at Burnley, O'Shea came off the bench to help his side secure a clean sheet.
The centre-back then put in another excellent display to help the Baggies secure a 1-0 win over Brighton on Saturday.
Ajayi was suspended for that match but the Nigerian international is now available for the visit of Everton on Thursday.
But Allardyce admitted he may stick with O'Shea with the boss having been impressed with the Republic of Ireland international who he previously asked to fill in at left-back and right-back.
"Absolutely – we got a clean sheet and Dara has performed very well," Allardyce said when asked if O'Shea has given him a selection headache ahead of Everton.
"Dara was unlucky to be left out the side anyway. He did a job for us filling in in a few different positions and then found himself left out the team which is very disappointing.
"He wouldn’t have looked upon me as the kindest because it was me who shifted him about and then left him out.
"He must have thought if he had stayed where he was he would have kept his place in the side. But he is a good, honest, lad and tries to help the team out.
"But Semi and Barts (Kyle Bartley) were playing okay."
Allardyce struggled to find a settled back four in his first 10 Albion games.
But after impressive performances against Manchester United, Burnley and Brighton, he feels Darnell Furlong, Conor Townsend, Bartley, Ajayi and O'Shea have all stakes claims for a regular spot.
"No back-four members have really been safe with their position in the team while I’ve been here until recently," the boss said.
"That’s obviously the Man United game, the Burnley game and the Brighton game.
"We have shown more consistency with our defending in those three games than we have in my entire time here.
"We had been shocking at times but we are getting better in that department."