Aaron Ramsey hit a hat-trick in the rout for the Gunners.
Allardyce said: "It was a disaster. I think I have a lot of trouble with the players taking onto the pitch what we asked them to do. Consistency has been a worry since that burst when I came in, the fact we can perform at that level against Leicester then dip so low in the first 45 minutes against Arsenal.
"The longer and longer I go on, the players are showing so much inconsistency that I face an uphill battle trying to get them to play at their best week in, week out. It was a pathetic first-half performance."
The manager continued: "You set out to block the areas Arsenal like to play in, we had the same gameplan that Swansea had on Tuesday. We studied how Swansea played, how defensively sound they were and how they limited Arsenal to very few chances.
"Swansea only had 30% possession but created chances, but I may as well have been talking in a foreign language. We didn't implement my plans either defensively or offensively and the game was dead and buried.
"It doesn't matter what system I pick, it's about players playing to their best. You can show them but it's up to the players.
"I'm not frustrated, I'm angry, very angry at the players performing to that level. It's unacceptable."