The Baggies endured a poor 3-0 home defeat to rivals Aston Villa during the first match of Allardyce’s time at the club.
Matters were not helped by Jake Livermore getting a red card early in the game.
“Yes I am upset – I couldn’t be anything else other than upset,” Allardcye told reporters when asked about Livermore’s red.
“When I arrived one of the first things I said to the players was ‘lads one thing we can’t have is any more sendings off.’
“So it really is very disappointing.
“They had a couple before I arrived. I’ve done my homework. That can’t happen again if we want to get out of trouble.
“And we have got to stop letting in easy goals – which Villa’s first one was. It was easy.
“I really need to work as quickly as I can and as often as I can on these elements.
“I just won’t accept another sending off no matter what.
“If we keep doing that we’ll have no chance of getting out of trouble.
“But what I can do is keep working on the lads not allowing the opposition to score easy goals.”