The Hammers consolidated their place in fifth in the Premier League after first-half goals from Kevin Nolan and James Tomkins cancelled out Craig Dawson???s opener for the home side.
Allardyce, who raised a smile as the travelling support sang ???We???re going to win the league??? after the final whistle, believes his side can challenge for the European places but wants his players to stay focused as they get set to embark on a hectic festive season.
He told Sky Sports News HQ: ???We???re on form for it [Europe] at the moment and if we can keep that form up yes, but like I said we won???t move our predictions on until mid or the end of January once we???ve got Christmas out the way.
???We don???t want these lads to get over-confident or get carried away and we want to make sure they look after themselves in between now and Sunday.
???If we can have a good Christmas, it hasn???t been like that for the last two seasons, steer clear of injuries and keep the players coming back then who knows what we can achieve in the second-half of the season.”
West Ham???s win means the East Londoners have suffered just one defeat in their last eight league matches and against West Brom it was the visitors??? defence which shone.
The Baggies, who had four strikers on the pitch towards the end of the game, piled the pressure on in the second-half but the Londoners held firm with Allardyce, who hopes to have Mark Noble, Alex Song and Diafra Sakho back in the squad to face Swansea on Sunday, delighted with his side???s determination.??
???I haven???t played a game away from home and had five attempts on target and five off target in one half so I think that shows how much we dominated after going a goal down,” he said.
???It became very scrappy second-half and then for us it becomes a case of keeping the back door shut and we did just that.
???It wasn???t very pretty at times but we dug it out and it???s a huge three points away from home at West Brom.???