Warnock was relieved of his managerial duties after four months in charge following Palace's 3-1 defeat to Southampton on Boxing Day.
Keith Millen has overseen two goalless draws in caretaker charge, leaving Palace in the Premier League relegation zone, with Newcastle United boss Alan Pardew set to take over permanently.
Palace launched a remarkable surge up the table last season under Tony Pulis after Ian Holloway oversaw a stuttering start.
And Parish believes similar impetus needs injecting into the Selhurst Park club's season if they are to beat the drop for a second straight season.
"We probably didn't get the right fit with Neil. We've got to take it on the chin with that one," the co-chairman told the club's official website.
"History will judge [whether it was the right thing to do]. Neil is a very, very nice guy and I would have loved him to be a success.
"I just think that we were drifting away again from what we're good at, and I don't think it's a time to change things, personally.
"We tried to play a different formation against Southampton, and I felt we looked a bit lost at sea at times and the crowd went flat. It's different then to dig yourself out of that.
"There's a real sense that we might lose something that we've got. The Premier League is such a fantastic place to be, we all want to stay there. That's the aim, that's the priority."
