Palace co-owner Parish confirmed Warnock will have licence to strengthen the Eagles' squad when the transfer window reopens, despite a raft of September arrivals.
Warnock launched his second spell as Palace boss by setting a £7million club transfer record to bring in Scotland midfielder James McArthur from Wigan.
Parish will also let Warnock loose in January's market, but warned the club will not abandon the prudent principals that have underpinned their top-flight return.
"There's money available - if we get the right targets," said Parish
"But sometimes you don't have to spend money
"It's almost now like there's a league table of who's spent what
People believe that's how the real league table is going to finish
"We will look at opportunities where we can strengthen our football club.
"We're not going to sign players and Neil won't sign players that he doesn't think are better than anybody we've got
That would upset the apple cart.
"That's not easy, signing players that are better than what you've got and then your academy kids coming through, it's not easy.
"We've built this club by taking people fundamentally that no one else wanted.
"The core group that are performing in the Premier League, for whatever reason have been undervalued."
Parish believes mainstays like Jason Puncheon and summer recruit Martin Kelly from Liverpool prove Palace's ability to help top-flight strays find a Premier League home in south London.
The Palace chairman admitted even he was caught out by football's inflated transfer market when ex-manager Tony Pulis championed the arrival of defender Scott Dann.
"Scott Dann is a fantastic player
He's a much, much better player than I thought he was, I must admit," said Parish.
"Credit to Tony Pulis: he always liked him when he was at Birmingham.
"There's value in the market place everywhere if you look at it
Maybe sometimes you have to find it
"That's the difference: we have to find it
It's a very imperfect transfer market
"If you're not playing for six to eight months or happen to be playing in a bad side, you just get forgotten about and nobody wants you.
"It doesn't mean you're a bad player
We've had to look at value from the first point when I came into the club.
"We know right now there's a certain type of player
If you look at someone like Martin Kelly, he has an England cap, he's been through some injuries like a lot of younger players do.
"He hasn't been playing regularly for Liverpool and England but you don't suddenly become a bad player overnight.
"We figure that it's a risk worth taking
We can't go and pay £5-10million for players in those types of positions."
Midfielder Puncheon's public spat with Warnock last term could have destabilised the new manager's eve-of-season arrival.
Warnock criticised Puncheon's missed penalty against Tottenham, with the pair trading public insults and landing in hot disciplinary water.
Parish praised them for settling their "stupid differences", with ex-Southampton midfielder Puncheon maintaining his impressive Palace form.
"They're two grown ups, they had a chat and went out to dinner and they've sorted themselves out," said Parish.
"Every single person that meets Neil realises that he's not that person people think he is.
"It's all behind us and Jason has been absolutely amazing for our football club.
"When you watch what he does week in, week out, how hard he works for the team, that hasn't changed one bit.
"Any stupid differences they've had have all been settled, so it's absolutely fine and credit to both of them really."
Source : PA
Source: PA