Four pitch invasions occurred during the game at the London Stadium, and co-owner David Sullivan was forced to leave after being hit in the head with a coin, with hundreds of supporters congregating in the stands below in protest at the club's board.
Parish showed solidarity with the West Ham owners, and believes that fans should understand the hard work Sullivan and co-owner David Gold are putting into the club.
"I do not wish what happened at West Ham on anyone," Parish told the Evening Standard. "I do not look at that and think 'that is great for us'. I know David Sullivan and David Gold. None of us are going to get this right in everything we do. It is impossible.
"I know those guys have got their heart and soul in that club. These are nice people who do everything they can for that club. Things do not go wrong on purpose.
"I understand people get angry but I think we have got to keep some perspective. This is meant to be fun. Three teams have got to get relegated. And everyone is trying as hard as they can to stay in the league."
Palace currently sit 18th in the Premier League table, facing an away game against Huddersfield Town on Saturday which could take them above West Ham in 16th place, should they leave with a win.