Burley was axed after the 3-0 defeat by Millwall on New Year's Day which left the Eagles second bottom in the Championship.
Since Parish handed the reins to Dougie Freedman, Palace have climbed out of the drop zone and are now seven points clear of third-bottom Sheffield United.
Parish told the club's official website: "I don't think anybody right now would say we hadn't done the right thing.
"George could have turned it around, but I felt at the time we were playing high-risk football and we couldn't guarantee survival that way.
"What Dougie has brought is the priorities we need in terms of being solid and difficult to beat. I think to that end it was absolutely the right thing to do."
Source: PA
Source: PA