Sunderland lost 1-0 to West Ham United at Upton Park yesterday.
The Black Cats were beaten 1-0 by the Hammers yesterday, but the North East club had enough chances to get something out of the match.
Jermain Defoe, Wahbi Khazri and Jack Rodwell all missed presentable opportunities, and Allardyce admits that his side cannot afford to miss so many chances, given their precarious position in the Premier League table.
"You can't create that many chances and not come away with a result,” he said.
"We are kicking ourselves, which is worrying, when you play that well and don't get any points. We are making life extremely difficult for ourselves.
"We did enough to win, never mind draw. It must be that black cat we ran over.”
Sunderland ended up having 13 shots at Upton Park, compared to West Ham’s nine, but the hosts showed greater ruthlessness in front of goal.
Michail Antonio scored the only goal of the match, when he slotted in calmly in the first half.
Sunderland’s performance was encouraging, but they have been guilty of playing well and not winning too often recently.
The Black Cats also dominated against Manchester City, but were beaten 1-0 by Manuel Pellegrini’s side earlier this month.
Sunderland’s defeat to West Ham leaves them stuck down in 19th place in the Premier League table.