The Eagles are currently in 19th place in the Premier League table after one win from their opening six matches.
Despite the team's early-season troubles, Parish is confident that Holloway is the right man in charge at Selhurst Park.
"I believe in the manager and I believe in his ability to create a winning team," he is quoted as saying by the South London Press.
"I've got every faith in Ian to sort it out. There are a lot of new players and we're trying to find both a formation and a way of playing.
"I know we're good enough to stay in this league. We just need to find a bit more of a goal threat and believe."
Holloway was appointed Palace manager in November 2012 before helping the club gain promotion to the Premier League later that season.