Claudio Ranieri's men cemented a seven-point lead at the top of the table on Wearside last Sunday when a fifth successive clean sheet paved the way for a 2-0 victory which left them with one hand on the trophy.
It might have been a very different outcome at the Stadium of Light had Black Cats midfielder Jack Rodwell not spurned a glorious 82nd-minute opportunity to cancel out Jamie Vardy's opener, while chances went begging too in the 0-0 draw with West Brom the previous weekend.
However, to Allardyce's consternation, that is the only clean sheet his side has kept in 18 league outings, and he is certain that addressing the defensive failings could prove hugely profitable.
Asked if his side needs to find a killer instinct in front of goal, the 61-year-old replied: "After the last two games and not scoring, yes.
"But I still think at this late stage of the season, it's rare when you are in this position that you score more than one, so clean sheets are still a lot of my big focus with the players.
"The more clean sheets they keep between now and the end of the season, the better chance they give themselves to survive because one goal will win them three points.
"If they want any explanation why I keep going on about that, look at Leicester - five clean sheets on the trot extending their lead in the Premier League.
"Other teams who have got better players, who play what everybody would call more entertaining football, if you like, it doesn't really matter to Leicester because they are the ones who are producing the results."
Saturday could go a long way towards deciding Sunderland's fate when they head for 17th-placed Norwich knowing victory would drag them to within one point of the Canaries with a game in hand.
Anything less, however, could prove enormously damaging and even if they do manage to keep that elusive clean sheet, they will need to find a finish at the other end to collect the win they crave.
Leading scorer Jermain Defoe has only found the back of the net three times in his last 11 appearances, although Allardyce insists his team-mates cannot leave it all to him.
He said: "Everybody needs to chip in - Jack should have chipped in last week, shouldn't he? He should have been the hero
Unfortunately, he put it over the bar."
This is the fourth successive season at the end of which Sunderland have found themselves scrapping for survival.
By popular consent, the current squad is the strongest they have had during that period, but Allardyce knows only too well that that guarantees nothing.
He said: "That's the trouble, isn't it? It's a strange game, isn't it? Is it the time when we can't get out of trouble, even though we maybe have a better team than those? Only time will tell."
Source : PA
Source: PA