The Baggies have been a side transformed in recent weeks with Allardyce's men first putting in an excellent display against Manchester United.
Then they then followed that up by dominating Burnley on Saturday despite having Semi Ajayi sent off after just 30 minutes.
Albion created numerous chances at Turf Moor. But the clean sheet was their first away from home this season and also the first achieved under Allardyce.
And he said they will have a chance of reeling in the likes of Newcastle, Brighton and Burnley if they continue to keep things tight at the back.
"The defensive side is getting better and better, we need to keep that nice and tight," Allardyce said.
"If we get eight or nine clean sheets from the next 13 games, we’ll have a chance.
“What we have to do is keep applying ourselves as well as we have done and be consistent in our performances and get a little bit better each game.
"Certainly we have to get more clinical in front of goal.
"The sad thing is since I’ve been here we’ve only won one when we should have won at least four and the last two.
"Next week becomes an even bigger task to try to go out and win because it’s a need to win now basis.”
Ajayi's red card at Turf Moor was unfortunate with the defender handling the ball around 40 yards out in a desperate bid to stop Burnley breaking following a poor pass from Conor Gallagher.
But while the Nigerian international had to go by the letter of the law, Allardyce felt it was another example of VAR interfering with the game too much.
"The rules today, everyone is going to say it’s a deliberate handball – that it’s stopped a goalscoring opportunity," Allardyce said.
"I can’t tell from 50 metres away that it’s stopping a goalscoring opportunity.
"People will say it’s right, because we’re just living with it aren’t we? We’re living with the rule changes, whatever happens now – we’re just living with it.
"If that’s the way the rules are then fine, we have to accept that, but I think it’s a handball that could’ve been avoided.
"Unfortunately he got sent off, but I have to say it didn’t affect us. You could say we got better with 10 men."