The hotly anticipated Tyne-Wear derby finished 1-1 at St James's Park after Aleksandar Mitrovic cancelled out Jermain Defoe's first-half volley.
It was the second successive Premier League match that Sunderland have thrown away a 1-0 lead and Allardyce was left frustrated with his side, who had dominated until the hour mark.
"We are our own worst enemy at the moment," said Allardyce.
"I feel that today we came and started the game particularly well and controlled the game in the first half..
"We created chances to score more than one and should have done. We know we needed more than one.
"Our stats show we need two goals to win a game and because we didn't score that second one on the chances we created in the first half we have ended up trying to protect what we have got.
"We fell foul to, it wasn't really a mistake but there was a lot of things we could have done to stop that cross and we end up frustrated with a point instead of three."
The draw leaves both sides in the relegation zone following Norwich City's win over West Brom and Allardyce was left to rue four points thrown away in successive Premier League matches away from the stadium of Light.
"It makes life very difficult for us," said Allardyce.
"Four points thrown away. At Southampton and here. out those four points on the board and we are feeling like we are going to be suriving.
"Now it will go right to the wire to stay safe. I can be content with the performance in taking control but I am frustrated we have not won enough games.
"We should have won this and didn't."