The Gunners followed up a 3-1 defeat against Liverpool at Anfield last week with another sub-par defensive display against Spurs.
The visitors raced into a 2-0 first-half lead thanks to a Christian Eriksen tap-in and a Harry Kane penalty, before Alexandre Lacazette halved the deficit with a well-taken goal just before the interval.
Pierre-Emerick Aubameyang equalised for the hosts in the 71st minute, but neither side could find a winning goal during an end-to-end finale at the Emirates.
Sokratis was slow to react when Leno parried away Eric Lamela's tame effort early in the game, allowing Eriksen to steal in and open the scoring.
Granit Xhaka, meanwhile, was guilty of a reckless challenge on Son Heung-min in the box, which resulted in Kane doubling Tottenham's lead from the spot.
Luiz, who was widely criticised for his performance at Liverpool, bemoaned Arsenal's latest set of costly errors at the back, before insisting he is giving his all to the team's cause.
"I think [the criticism] is normal, in my all my career it has been like that, especially when you are a defender," he told Sky Sports.
"Strikers never lose games unless if they miss a penalty in the last minute, this is football.
"The defenders have to take responsibility and take [criticism] in a good way, in a humble way. We need to understand when we make a mistake and say that.
"I'm going to try to do my best always. My game until the penalty at Liverpool was very good, especially for our first big game.
"Today, even with pain I played the whole game and tried to show spirit until the very end.
"I am trying to improve with the team every single day. You have to be mature to understand this kind of moment."
Arsenal sit fifth in the Premier League table after four matches of the 2019-20 season, with the international break now set to take effect.
The Gunners face Eintracht Frankfurt four days after making the trip to Vicarage Road, with Standard Liege and Vitoria also joining last term's finalists in Group F.