Two goals in three first-half minutes through Matheus Pereira and Matt Phillips put Allardyce’s men in control at the Hawthorns before Callum Robinson’s fine finish completed the Baggies’ biggest home win in the Premier League since November 2016.
It is one of many top quality performances over the past eight or 10 games but we haven’t received the credit because we didn’t win, We have missed out on many points due to our poor finishing, Allardyce said.
We have had two very important wins but unfortunately we have to rely on other people losing.
But we are still fighting.
The victory was made more admirable by the fact West Brom needed to rally after having what would have been an opening goal for Mbaye Diagne controversially ruled out for offside after video assistant referee Kevin Friend decided there was insufficient evidence to overturn the on-pitch decision, even though TV replays suggested otherwise.
Sam Johnstone completed an excellent evening for West Brom when he turned away James Ward-Prowse’s injury-time penalty.
West Brom are still in deep trouble, eight points adrift of fourth-bottom Newcastle with seven games remaining.
However, if they meet many more sides as accommodating as Ralph Hasenhuttl’s Southampton were in a dismal opening period, another of Allardyce’s great escapes cannot be discounted.
It gives the players hope and belief,” added the former England boss.
We have slipped up in front of goal too much. We would be on the 30-point mark now if we had taken our chances.
We have got it down to eight points but games are running out.