James Milner opened the scoring from the penalty spot in Monday's Premier League game after former Reds defender Mamadou Sakho was harshly adjudged to have brought down Mohamed Salah in the box .
Salah drew a foul from Aaron Wan-Bissaka that saw the young right-back dismissed before the Egypt star sent Sadio Mane clear to wrap up the points in injury time.
An angry Hodgson disagreed with Michael Oliver's decision to award Salah a penalty and said Palace should have had a spot-kick of their own when Max Meyer went down in the box.
"It wasn't a penalty. I've been in football a long time, and if that is a penalty then the game has changed beyond all recognition," Hodgson told a news conference.
"Mamadou is trying to defend and there is no way he is looking to foul the player or get contact on him at all.
"If people can't see that then I'll be the pariah who sees only what he wants to see, and if all you guys see it as something different then I'll accept it.
"I don't want penalties for my team in that way – if you ask me one day 'was it a penalty' and I don't say that those situations aren't penalties both for and against, then I'll be very disappointed in myself and you'll be quite entitled to take me up on it.
"I'm frustrated because I don't think that's a penalty. I also don't think it was a foul on James Milner when we had a counter-attacking chance, and I do think it was a penalty in the last minutes when Max Meyer gets wiped out in the area by [Virgil] van Dijk when he was about to get a touch on the ball, but these things happen.
"Sometimes refereeing decisions go against you and it's disappointing and a cause for frustration and anger, but if you ask me about the team's performance I think it was very, very good.
"I take some comfort and pride in that, but it's not going to change my disappointment and anger at how we came in at half-time losing 1-0."
Hodgson accepted Wan-Bissaka's red card, though, the otherwise impressive 20-year-old bumping Salah to the ground after chasing down the Liverpool attacker as he ran through on Wayne Hennessey's goal.
"It's one of those things," the former England boss said. "We were pushing to get an equaliser, playing quite well, looking reasonably likely to get a goal and were asking questions of the Liverpool defence, but then from a ball lumped forward we didn't win the header and we were light at the back.
"Aaron did his level best to try and get back in and stop Salah from going free with the goalkeeper. He definitely touches him so there's no question it was a sending off, but I don't think he was looking to clip his heels – he was genuinely trying to get his foot on the ball but didn't succeed.
"As a result he caught the player and the referee was right to send him off."