Snodgrass went to ground despite Scott Dann appearing to miss man and ball with his challenge, but referee Mike Jones pointed to the spot and the Scotland international scored his fifth Premier League goal of the campaign.
Palace boss Alan Pardew said after the game that Snodgrass would be "embarrassed" when he watched the replay, and the 29-year-old was quick to hold his hands up after the full-time whistle.
He posted on Twitter: "Apologies from my end it was never a penalty, but genuinely thought defender was going to slide, so tried to ride the tackle."
REPORT: Hull City 3 Crystal Palace 3: Frazier Campbell returns to haunt Tigers in six-goal thrillerIt was the first of six goals at the KCOM Stadium as the Eagles were involved in another high-scoring thriller, two weeks after their 5-4 defeat at Swansea.
Pardew was frustrated his side needed a late Fraizer Campbell equaliser, despite having led 2-1 with 20 minutes left, but he feels Snodgrass let himself down with his simulation.
"Fabrication would be the word I'd use," Pardew said after being asked for his view of the incident. "I think we all want it out of the game.
"I said to the referee, 'I'm going to defend you'. It's difficult at match speed to call that right. He gets that wrong.
"But Snodgrass really needs to have a look at himself in that situation. I'm sure when he looks at it back on Match of the Day he'll be embarrassed."
Hull boss Mike Phelan would not criticise his player in public, but admitted he would probably have been aggrieved had the decision been at the other end.
He said: "The referee is the man in the middle who makes a decision. I'm not going to pull my own player up for something that the referee gave. I'm sure Alan is aggrieved by it, as I probably would have been at the time, but we take what we're given at this level."
When asked if he would have a word with Snodgrass, Phelan added: "That may happen next week, but right now I've just come out of a disappointed dressing room after my players showed fantastic attitude and effort. And I'm not going to pick holes in certain situations."
Snodgrass' penalty gave Hull a 1-0 lead at the break, but, after Palace mirrored the hosts' three-man defence at the interval, the game sprung to life.
The excellent Wilfried Zaha was brought down in the area by Snodgrass, allowing Christian Benteke to equalise, before the former Manchester United winger produced a brilliant piece of skill to make it 2-1.
Hull profited from some poor defending to turn the game on its head again, with Adama Diomande levelling before Jake Livermore added a third.
But former Hull striker Campbell popped up in the 89th minute to earn Palace a point.
Pardew said: "When we take a 2-1 lead we should see the game out. We needed Fraizer to get us a very important point.
"I said to my staff before the game I fancied Fraizer today if we need a goal."
Phelan was frustrated as his side scored three goals for the first time in the league this season, but failed to pick up all three points.
He said: "A win would have been massive. But when you score three goals at home and you don't win a game of football at this level then you have to find the few negatives."
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