West Ham finished 10th in the Premier League last season, but they now sit just outside the relegation zone after winning just one of their opening six games.
The Hammers have sorely missed the injured Andy Carroll, who is out for an indefinite period of time because of a heel injury.
Allardyce admitted on Friday that his team will have to accept being called relegation candidates while they continue to fail in front of goal and he wants to see an improvement.
"We have created chances, but we have lacked the ability to score them," the West Ham manager told a press conference.
"Hopefully, Andy will change that when he comes back, but the other players can't keep missing as they are at the minute.
"That is the key element. We have to keep believing that those chances will eventually go into the back of the net and to keep creating them.
"All the players who have been getting these chances away from home have failed to put them in the net and that's why we are suffering the consequences now.
"We have had three games away from home with a magnificent defensive record - one goal conceded which was a penalty which was wrongfully given.
"That is something to really build on but at the other end, unfortunately we couldn't marry it up with a goal or two as we should have done.
"Six or seven points away from home would have been a fairer total than only two."
There was much enthusiasm surrounding Maiga when he signed for West Ham from Sochaux in 2012, but he scored just two league goals last term and he is yet to find the net in seven matches this year.
When asked whether he was worried about the Mali striker's form, Allardyce pulled no punches.
"Absolutely," the former Blackburn boss said. "I would like him to have scored a few more goals and made a bigger contribution, but that's not been the case."
West Ham's situation is so desperate that it looks increasingly likely that they will re-sign free agent Carlton Cole just four months after they released him.
Cole, who was at West Ham for seven years, has been training at the club's training ground in Chadwell Heath and he looks set to sign a short-term deal if he comes through a behind-closed-doors friendly next week.
"I said last week that Carlton is joining in training with us and we have a planned game behind closed doors next week while the international break is on," Allardyce said.
"When he has come through that game, hopefully he'll be looking fitter and after that game we see that he can make a big contribution to us. If that is the case, there is already a contract there available."
West Ham will have to be at their best on Sunday to unlock a Tottenham defence that has conceded just two goals so far this term.
One crumb of comfort for Allardyce is that he is likely to have Joe Cole, who scored against Spurs last term, available following a five-week hamstring injury lay-off.
Allardyce said: "Joe is not ready to start, but we hope he will be involved in the squad depending how the next two days of training go.
"If I can get him on the bench that would be very good from our point of view because you want all your players fit and available for selection."