Palace had accepted a £35m offer fot the England defender and a medical was planned before the Eagles pulled the plug hours before the deadline.
Parish told talkSPORT on Sunday: “It's a difficult decision. It's as simple as that these things are never black and white.
“I decided in the end that, based on the advice that I got and with what I think, that we would have a better season if we kept Marc.
“We don't guess about these things. If you look at it rationally, if you look at what is worth the place in the Premier League, the fact that we're in the Conference League for the first time in our history, this is a fairly unusual set of circumstances in which to keep a player.
“If we were fighting between the difference of 10th and 14th, if that was going to be the difference between keeping Marc and letting Marc go, then probably we would have said right, 'We should take the money.'”