Sunderland remain in the relegation zone but showed spirit in fighting back from two goals down to earn a draw at Anfield.
The Black Cats fought back from 2-0 down in the final 10 minutes at Anfield to secure a 2-2 draw against Liverpool but they still remain in a fierce battle for survival.
With Newcastle United winning at the weekend, Sunderland are four points adrift from safety with Norwich City dropping to 18th.
Allardyce is quoted in the Northern Echo, saying: “I think from the 13 games we need six wins. They have done it before, haven't they? They're good at miraculous recoveries here – let's hope we are again.”
The goals from Adam Johnson and Jermain Defoe showed there is an element of belief in this Sunderland side as they fought back following a pretty dismal performance prior to that, as they were opened up and looked lethargic time and again, but Liverpool failed to punish them even more.
But it's certainly a point gained for the Sunderland boss, who added: “It could be a big point. We've still got an awful long way to go but a point here is precious, especially under the circumstances. If the lads can show that sort of spirit and never-say-die attitude they've got a good chance.
“If they can start playing like they did on Tuesday night, and play with that type of spirit and score goals like they scored at Liverpool, they've a good chance of getting out of trouble. Our games are running out.
“A draw was good enough because nobody would have expected us to get a draw. That precious point will hopefully start leading to a victory very, very shortly because we need to start putting a few three-pointers on the board.”
After the performance against Manchester City, where they were unlucky to lose, and the fightback at Anfield, there may be a little bit of momentum generated off the back of those two games, going into another challenging encounter when they face Manchester United at the weekend.
Certainly, they have shown that maybe they do have a place at this level and the Premier League is where they ought to be playing their football, now they need to get the points on the board between now and the end of the season to back that up.