Sunderland lost their latest match 1-0 against Southampton.
However, they were much tighter at the back against Southampton in their latest outing, until Yann M’Vila gave away a needless penalty.
And Allardyce said: "Until we start cutting out silly mistakes like that, we'll be fighting at the wrong end of the table. Yes, Southampton were the better team and had the better chances, but we've got to stop gifting games to the opposition.
"The game was 0-0 at that point, and who knows, we might have broken up the other end and nicked a winner. If we came in at 0-0, I'd have been very happy today based on the performance we gave."
Allardyce made changes to Sunderland’s system against Southampton, as he looked to limit the chances that the opposition could make at the Stadium of Light.
Sunderland conceded six goals against Everton two weeks’ ago, and that performance was not a typical one for an Allardyce side.
Allardyce is renowned for his ability get teams organised, and the Black Cats were well on their way to claiming a good point against Southampton yesterday.
However, M’Vila’s error consigned them to another defeat, and they are falling under even more pressure to start turning their form around, with the Wearsiders now four points away from safety.