Mac Allister was dismissed by referee Thomas Bramall after catching Bournemouth’s Ryan Christie with a high boot in the 58th minute at Anfield.
It was a dubious decision that ruined Mac Allister’s home debut for the club after the Argentina midfielder’s close-season move from Brighton.
Liverpool still managed to secure their first Premier League win this term as goals from Luis Diaz, Mohamed Salah and Diogo Jota cancelled out Antoine Semenyo’s third-minute opener.
But Reds boss Klopp was frustrated with Mac Allister’s dismissal and could try to get it overturned.
“I think the amount of times I was asked about it shows it’s worth discussing again, which we will probably do,” Klopp said.
“I asked Macca and he said, ‘I touched him but not really’. That’s all he told me.
“After the game I saw it back. I think if you have a list of points, what we need to give a red card, besides contact there’s nothing else, no other boxes ticked.
“VAR would not overturn it because contact means it’s not a clear and obvious mistake.
“Now the punishment, 40 minutes with 10 men is already punishment enough. But let’s see, we have to talk to the authorities.”
Liverpool were leading 2-1 when Mac Allister was sent off, but far from retreating, they seemed fired up by the sense of injustice, with Jota scoring the third four minutes later.
Following their 1-1 draw at Chelsea last weekend, Klopp acknowledged this was another erratic display from Liverpool.
“The start of the game was obviously not how we wanted it,” Klopp said. “We conceded the first goal after a minute and then it was offside so you think that’s the wake-up call we needed.
“Then we concede another goal two minutes later and then there’s a yellow card for our goalie so it’s not what you need but you are working with human beings so you have to figure it out.”
