The Baggies followed up their emphatic 5-2 win at Chelsea by thumping Ralph Hasenhuttl’s men 3-0 last night.
The could have won by an even bigger margin with Albion creating a host of clear-cut chances during a first half in which they were rampant.
But while they have played well in their last eight games, they remain eight points from safety after Newcastle beat Burnley on Sunday.
Allardyce admitted that win for Steve Bruce’s side was a hammer blow for his team.
But he says their outstanding performances, particularly their last two, will have everyone in the Premier League standing up and taking notice.
“It’s one of many top-quality performances over the last eight or 10 games,” Allardyce said when asked about his team’s display against Southampton.
“But before that, because we hadn’t won the games we should have won, we didn’t get the congratulations we have got from the last two.
“We have won 5-2 at Chelsea with a brilliant, outstanding, performance and we have now won 3-0 against Southampton. Again it was another outstanding performance.
“We have had many outstanding performances but too many times there hasn’t been three points at the end of it.
“We have missed out on many, many, points because of poor finishing. Because of that, we are left in this position.
“But at least it’s two wins, back-to-back wins, and two very good performances.
“They are two wins that are pricking people’s ears up - people are saying ‘look how good West Brom have got, look at what players they have got, look at the football they are playing, look at the finishing they are producing now.’
“We have to now keep that up in the next game and the next game.
“Unfortunately for us, we have to rely on other people losing as well as us winning.
“All we can do is win the next game and then keep our fingers crossed those teams above us don’t win.”
Albion were hugely unfortunate not to take the lead after just four minutes against Southampton when Mbaye Diagne nodded in from close range.
The goal was initially ruled out for offside before a VAR check.
Incredibly, VAR officials in Stockley Park then deemed there weren’t enough cameras available to determine whether or not Diagne’s upper body was onside or offside - the call was that right.
And that meant his header was ruled out with the officials deciding to stick to the original on-field decision.
“VAR failed us,” Allardyce said.
“It failed us massively.
“I’m sure everybody has seen it.
“And the thing is, the big man is so disappointed he’s not got another goal.
“He is a goal scorer and when goal scorers get goals they are happy and their confidence soars.
“When they get them taken away, which they don’t deserve to get taken away, it can affect them.
“We saw his delight when he scored at Chelsea and he should have been allowed that goal tonight.
“His brilliant assist for our second goal would have been the perfect night for him.
“But because he has been denied that goal he is pretty miserable in the dressing room, unfortunately.
“I’ve looked at the camera angle. We’ve got about 16 cameras here and it was onside.”