Liverpool visited Selhurst Park on Monday night seeking to build on the opening weekend win over West Ham, in which Salah bagged.
And they had the added incentive of needing to keep pace with title rivals Chelsea, Tottenham and Manchester City who all won over the weekend.
Liverpool struggled to find a way through Palace’s resolute defence in the first half but went ahead on the stroke of half time thanks to James Milner’s penalty.
Milner converted the spot-kick won by Salah after the Egyptian had been on the receiving end of a challenge from Mamadou Sakho.
Debate raged over whether referee Michael Oliver should have awarded the penalty due to the minimal contact involved.
Allardyce has now revealed the thought process Salah had which he says led the winger to decide to go down in the box.
“I’m not having it but it’s like anything else,” Allardyce told beIN SPORTS.
“You can buy a penalty if you feel a contact.
“But for me he could have easily stayed on his feet.
“But he’s felt the contact and thought: ‘Well, instead of staying up, I’m not scoring here so I’ll go down.'”
Allardyce offered an extended take on the incident after Sadio Mane’s goal had wrapped up a 2-0 Liverpool win, adding: “There’s not enough contact to make him fall over.
“He falls over but it’s still a penalty because he makes contact and the referee’s given it.
“So it’s a penalty.”
Manchester United legend Gary Neville gave his verdict on the penalty, singling out Sakho for criticism.
“It’s one of those ones where if it was a player in your team, you’re saying: ‘Go down and win the penalty’,” Neville said.
“I think Salah does.
“It’s theatrical, people won’t like us saying that, they’ll be offended.
“But if it’s against you, you think it’s soft.
“One thing I would say is there has been a mistake made by Sakho. He’s too tight, he’s clumsy, he’s all over him.
“There’s a stamp at the ball first time, then there’s a double one there.
“You just see there that Salah’s got his right leg hanging and it is a theatrical fall, which to be fair we’ve seen a lot of players do, but it’s clumsy from Sakho.
“He’s given Salah a decision to make.
“I think what he’s doing there Sakho is he’s had a first little tackle and look how split his legs are.
“He’s had a little nibble again, a second nibble.
“He’s gone the first time, he’s fine, but he lifts his leg and goes again.
“He’s lost control of the tackle, it’s desperate, it’s a little bit rash.
“But there’s no doubt Salah takes it, look at that fall, he just collapses.”
Liverpool will be eager to maintain their 100 per cent record when they face Brighton at Anfield on Saturday.