The Gunners were in the ascendancy from the start as they took the lead through Pierre-Emerick Aubameyang on the 21st minute mark, but Jamie Vardy's late goal helped the Foxes to snatch a late draw against 10-man Arsenal.
Arteta was gutted his side could not snatch the maximum points and insists they should have killed the game.
“We lost two points. I think we deserved to win the game. But when you have the chances you have to kill them,” the Spaniard told BBC Sports after his men failed to win for the first time in five games.
“Three or four-nil and the game is over. We had to play a long time with 10 men.”
The hosts were dealt a big blow in the 75th minute when Eddie Nketiah was sent off just minutes after coming on as a substitute for a challenge on James Justin.
The 37-year-old was angry with the decision to send Nketiah off and insists Vardy should have been sent off for a similar tackle in the first half.
Arteta added: “With the red card decision, he doesn't see the player and you have to know that he is a young kid.
"But if that is a red card then Leicester have to play with 10 men after 42 minutes. That has to be a red card as well."
Arsenal next face bitterest rivals Tottenham Hotspur in the Premier League on Sunday.
