The south London side's 3-0 home win over Southampton on Saturday helped them stay three points clear of the relegation zone after six league defeats in a row.
“Alan has a 41 percent win record at Palace which is pretty astonishing,” Parish told Talksport.
“It's totally safe (Pardew's job) in that every manager is under pressure. It's a binary industry and you have to win football matches.”
Parish said the team was no more in crisis than the other clubs struggling near the foot of the table and said everyone at Selhust Park was working hard to help Pardew succeed.
“We have to find the balance. There's plenty right and we just need to fix the things that are wrong,” he added.
“If we're in crisis then there are a lot of clubs in crisis. We need to get points on the board and everyone is behind Alan in doing that.
“He's a positive force around the football club. If you look at the league, the top teams have gone on to a different level but it's very flat at the bottom.”
Palace, who are 14th with 14 points, visit second-bottom Hull, who have 11, on Saturday.
Original source: Pardew’s job as Palace manager is safe