The Ivory Coast international was shown a straight red card by referee Anthony Taylor for a bizarre headbutt on Ezgjan Alioski.
It meant Arsenal were forced to play most of the second-half with ten-men.
Leeds were able to muster 25 shots, but only four were on target. Likewise, Arsenal only hit Illan Meslier's goal twice.
Gunners whizkid Bukayo Saka had the best chance of the game but was denied by a fantastic save from Meslier.
Asked about Pepe's red-card, Arteta said: "It is unacceptable. I've spoken to him; it is unacceptable.
"I really like the personality of the team. When Pepe let the team down, how we suffered together and stuck to what we had to do.
Reflecting on his side's performance, Arteta added:
"Considering how we got Pepe sent off, a draw is okay.
"I never like playing for a draw, but in the circumstances a point is okay.
"In the first 30 minutes we were more dominant and created a lot of issues. But then the game broke a bit and we gave the ball away in difficult areas.
"We suffered and in the second half we were early with 10 men and it was a matter of defending well and staying patient, and using the pace of our players and the spaces they were leaving."