He said: "We end up hugely frustrated with a point instead of three and that makes life again so difficult for us. It happened at Southampton and now it's happened here today - that's four points thrown away.
"But those four points on the board now and we are feeling like we are going to be surviving and we are going to stay safe. Now we are going to go right to the wire to try to stay safe, and that's the bottom line.
"While I can be content with the players' performance and taking control of the game today, I'm a little frustrated about the fact we have not won enough games and again should have won this one and didn't."
The international break means Allardyce now has two weeks during which to stew on another missed opportunity before West Brom head for the Stadium of Light.
He added: "We have got another two weeks to wait before we play again. We had a long wait to play this one when I wanted a game next week. Now we have got another two weeks for football associations to make money with stupid b****y friendlies."