The Baggies hosted Carlo Ancelotti's side at The Hawthorns last night and were the better team for long spells.
But they ultimately fell to a 1-0 loss with Richarlison netting the only goal of the game in the 65th minute.
Mbaye Diagne and Conor Gallagher had earlier missed good opportunities to put Albion ahead.
Allardyce's men were then denied a dramatic stoppage-time equaliser when Diagne fired in only for VAR to judge his foot offside.
That wasn't the only decision to go against the Baggies with Allardyce believing his team should have had a penalty when Diagne was tripped in the box by ex-Baggie loanee Mason Holgate.
Overall, though, the Baggies only had themselves to blame for not taking at least one of the chances they created.
And it means they remain nine points behind 17th placed Newcastle – with the two teams now set to meet in a crucial relegation six-pointer on Sunday.
"We now need to beat Newcastle on Sunday and get closer to the teams above us," Allardyce said.
"We can take heart from the performance against Everton and say to the lads well done, but it's all about points for us.
"No points is not what we are looking for.
"It's another game gone by where we are further away from fourth bottom because we've not got one game less."
Allardyce was hugely frustrated the Baggies weren't given a penalty for the challenge Holgate made on Diagne.
And the boss also felt his team was very unfortunate to see the striker's stoppage time goal ruled out.
"I’m disappointed for my players tonight and feel hard done by," the boss continued.
"Most of it is our own fault. But obviously some of it is the officials not giving us a penalty in the first few minutes.
"The tackle from Mason Holgate on Mbaye, I’ve been watching football while VAR has come in and I’ve seen 50-60 penalties given for less than that. Next week I’ll see two penalties given for similar incidents and it boils down to the lack of consistency.
"VAR is not making life consistent.
"That would have given us an opportunity to go 1-0 up. If we miss the penalty it’s our fault, if we score it we’re 1-0 up. And if we go 1-0 up I don’t think we lose this game.
"The players in the dressing room know we shouldn’t have lost the game.
"We should’ve taken our opportunities or created more opportunities."
On Diagnes disallowed goal, Allardyce said: "We scored a great goal, and it was half a toenail offside sadly.
"If you’re on the right side of that it brings you points, if you’re on the wrong side you lose points.
"We should have got a point and now we need to correct that on Sunday.
"It will be about mentality. Grit and determination and the size of your heart.
"We need to punch through the pain barrier because we will still be feeling the mental and physical exhaustion of the Everton game."