Johnson was named on the substitutes’ bench at Selhurst Park, and the winger was not impressed at missing out.
Allardyce says that the 28-year-old wanted to start in the fixture, but it seems that Johnson now faces a battle to win his place in the team back.
“[I left] Adam Johnson on the bench who wasn’t very happy – it may be that we play 4-2-3-1.
“For a struggling club we have got plenty of options going forward.
“We’ve got to be flexible.”
Johnson was left on the substitutes’ bench for the entirety of Sunderland’s match against Palace on Monday, but he would find it hard to argue that Allardyce made an error by overlooking him.
Sunderland managed to pick up a vital victory in London, with Jermain Defoe netting a late winner in the contest.
Sunderland’s win has moved them much closer to safety, and there is now cause for optimism at the Stadium of Light.
Sunderland’s next fixture comes against Stoke City, and a win on Saturday could lift them out of the Premier League drop zone for the first time this season.