Alexander-Arnold was lucky to avoid a red card in the first half at St James’ Park before Brooks sent off Virgil van Dijk for a later incident.
It all kicked off after just five minutes when former Everton star Gordon shoved Alexander-Arnold – with the Liverpool defender angered by Brooks’ decision not to give a foul.
That saw Alexander-Arnold petulantly throw the ball away as Brooks handed him a yellow card.
Just two minutes later and Alexander-Arnold could have been dismissed for putting his arm around Gordon and brining him down.
But Newcastle boss Eddie Howe and the home fans were left furious as Alexander-Arnold avoided the second booking.
Carragher, though, hit out at Brooks for not booking Gordon as he said on Sky Sports: ‘Listen, Trent deserves a yellow card. We know the rules, he throws the ball away, but it’s a really poor decision and the referee makes a rod for his own back.
‘How is the shove from Gordon not a foul in the first place? How the referee doesn’t give a foul there is absolutely unbelievable.
‘I think that’s why he doesn’t give the second yellow.’
Gary Neville @GNev2, meanwhile, speaking about Alexander-Arnold’s decision to foul Gordon just moments after being shown a yellow card, added: ‘He’s lucky. Would Klopp think about substituting him? It’s cauldron out there. He has sent out Joe Gomez to warm up. I’m not surprised at all. It must be a serious consideration.’