“Our performances, our final third opportunities, our defensive solidarity are all good enough to stay in the Premier League,” he said.
“The one thing that is not good enough is our conversion rate – that is why we are where we are.”
For a good few months now, Albion have struggled to put the ball in the net.
That lack of cutting edge is the reason why they failed to beat Manchester United, Burnley, Newcastle and Crystal Palace despite being the better side in all those games.
But just when it seemed all hope was lost, Albion’s forwards showed their quality to secure a result that nobody could have foreseen.
The statistics surrounding Chelsea prior to this game were well documented.
The Blues hadn’t lost in 14 outings since Thomas Tuchel replaced Frank Lampard as boss.
During that run they had conceded just two goals despite tough fixtures against the likes of Tottenham, Manchester United, Liverpool and Atletico Madrid.
But exquisite finishing from Matheus Pereira, Callum Robinson and Mbaye Diagne saw Albion put five past them and secure a deserved victory.
They were helped on their way when Thiago Silva was sent off just before the half-hour-mark after a reckless challenge on Okay Yokuslu led to him getting a second yellow card.
But as Allardyce correctly pointed out afterwards, Albion had been the better team even when Chelsea had 11 men.
And they won this because of the brilliance they produced in the final third – with all five of their goals exceptional.
The one thing Chelsea will point to is that – just before Silva’s dismissal – they had actually taken the lead.
A brilliant free-kick from Marcus Alonso saw the Spaniard smash the ball against the post from 25 yards. And it was Christian Pulisc who then reacted quickest to fire into an empty net.
That goal arrived in the 27th minute, just moments after Albion had lost Dara O’Shea to injury. Branislav Ivanovic replaced the Republic of Ireland international in Albion’s back three.
But following Silva’s red card, he too had to be replaced after pulling a hamstring in a foot race with Timo Werner.
It was the decision Allardyce made next, though, that proved to be this game’s biggest turning point.
For the first time in months, Allardyce opted to line-up his side in a 3-5-2 formation.
That was a very bold call with the Baggies having looked much more solid ever since the boss settled on the 4-3-3 system first used against Manchester United.
But the boss wanted to match Chelsea’s innovative 3-4-2-1 system as best he could.
And that proved to be the right call with his side bright and on the front foot during the opening 20 minutes.
When O’Shea had to come off injured, Allardyce simply swapped him with a like-for-like replacement in Ivanovic.
But when he too had to come off – the head coach decided to throw caution to the wind.
Initially, he did tell fellow defender Lee Peltier to get ready.
But then he changed his mind and introduced Robinson in a move that saw the Baggies switch to a 4-2-3-1.
That move proved to be inspired, with Robinson – who was deployed on the left wing – going on to put in an outstanding performance.
It was Pereira who turned this game on its head, though, when he then scored two stunning goals in first-half stoppage time.
The first was one Chelsea, and Tuchel, really won’t want to see again.
It was actually goalkeeper Sam Johnstone who claimed the assist with nothing other than a long punt forward.
But Pereira noticed Kurt Zouma had misread the flight of the ball.
He then noticed Edouard Mendy had come to claim only to effectively put himself in no man’s land.
And the Brazilian then produced a brilliant half-volley to lift the ball over the keeper and into the net.
Incredibly, Pereira was at it again before referee David Coote could blow his half-time whistle.
This time the forward collected a pass from Ainsley Maitland-Niles before keeping his composure to calmly roll the ball into the corner from 12 yards.
Both of Pereira’s goals were excellent.
But even with 10 men, a team like Chelsea would expect to battle back and earn a point.
Robinson, though, loves playing against the Blues. And just past the hour-mark he snatched the best goal title from Pereira in spectacular fashion.
Darnell Furlong collected the ball on the right before pinging in a wonderful cross.
And that was met at full speed by Robinson, who charged into the box before smashing home the most delightful volley.
In no mood to give Chelsea a sniff, Albion scored again just five minutes later.
A brilliantly-executed counter-attack ended with Conor Townsend finding Pereira in the box with a back-heel.
And he then squared for Diagne, who slotted the ball past Mendy from just inside the box.
To Chelsea’s credit, they pulled a goal back with 20 minutes to play when Mason Mount tapped in a cross from Werner.
But in stoppage time, Albion made the win emphatic when Pereira slipped in Robinson, who cheekily dinked the ball over Mendy and into the net.
Five goals in what was, without question, their best performance of the season, Albion had left Chelsea stunned.
As Allardyce said, their performances, their final third opportunities, their defensive solidarity were already good enough to stay in the Premier League.
Here, they showed they have the goalscoring ability as well.
Albion fans know, in reality, it’s likely this win has come too late.
But the confidence it will give the team and the forward players in particular cannot be underestimated.
And if they beat Southampton a week today, fans will start to dream the club who produced the great escape can better it with the greatest escape.