The Hammers returned to winning ways in the Premier League with a 3-0 victory over Hull at the Boleyn Ground.
Andy Carroll broke the deadlock in the 49th minute, Morgan Amalfitano doubled the lead on 69 minutes, and Stewart Downing wrapped up the scoring just minutes later.
Allardyce was delighted with his players’ performance against Hull and underlined the importance of the win.
“We've won this game and it was a very important win, because it gives us all a big lift ahead of the FA Cup fourth round next week, where we want to go as far as we can,” West Ham’s official website quotes the 60-year-old as saying.
“Clinical finishing has been missing, as have clean sheets, so my message to the team was 'Get it right in both boxes lads' and that's is what is really going to count," added Allardyce. "In the end, because we've done it because we got a clean sheet at one end and three goals at the other."
West Ham’s results over the festive were not great, which is why they had fallen behind in the race for a top-four finish in the Premier League this season.
However, the win against Hull has put the London outfit back in the chase, as they are now just four points behind fourth-placed Manchester United in seventh place.
The Hammers were favourites to win against a Hull side struggling against relegation from the Premier League, but even then, three goals scored and none conceded are commendable stats.
Having won their last two competitive games, the West Ham players are certainly high in confidence. The fans will now hope that the team can build on them and march towards glory.