After the game, a disappointed Allardyce was of the belief that for a second game in a row his team were unable to record maximum points having conceded to a late Virgil van Dijk goal against Southampton last time out.
"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," said Allardyce whose side sits third bottom on the Premier League table.
"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."