The Hammers were deeply embroiled in the fight for Baclays Premier League survival until a run of consecutive victories pulled them clear and left them in the top half of the table - with only a defeat at Everton blotting their record ahead of the international friendly fixtures.
Once the favourite to become the next manager to find himself out of work, Allardyce masterminded wins over Swansea, Aston Villa, Norwich and Southampton and is eager to see his side return to winning ways at Stoke on Saturday.
"The clinical aspect, which we done so well in the four games we'd won on the trot, deserted us at Everton and we've got to get that back," he said.
"We've got to take the opportunities when they arise, we scored against the run of play sometimes, we scored when we were in the ascendancy and we've to make sure we are as clinical as we were in those four games.
"I'm not sure about results because it will be tough to get better results than we've had. We have to try to achieve the results and improve the performances, the demand from me is a level of consistency from the players that will deliver results."
Mark Hughes' Stoke side are level on points with West Ham and will be looking to record a double over the Hammers after winning 1-0 at Upton Park in August.
That remains their only away league win of the campaign but a string of impressive results at home means Allardyce is wary of the threat the Potters possess.
"They mix up the service a little bit more than Tony [Pulis' team] did," he said.
"You've got a mixture of playing off Peter Crouch or through midfield. It's slightly different to how it used to be when Tony was there, but it's equally as dangerous in those areas as they always were. Our defensive unit has to be solid and aware of what they're going to try and do to break us down.
"When you're in possession you must retain that possession and then try to create opportunities against the opposition that you think you can expose. It'll be about our players playing their best there.
"I remember us having a fantastic result there last year, a 1-0 win with Jack Collison scoring. We go in in good form, even though we lost to Everton, we go with a lot of confidence and we've got to make sure we convert that confidence into a very good performance."
Club-record signing Andy Carroll was suspended for three of the four recent wins, only coming off the bench at Everton with his match fitness lacking.
Now the England striker could return to the starting line-up, with Allardyce stressing the need to have a strong squad behind his first team.
"My best XI have played recently and they've played exceptionally well," he said. "The form of those players was at their top level so they became the best XI, but nobody today looks at a best XI any more.
"You look at the strength and the depth of your squad and when needed, for whatever reason, to change the side and somebody can step in so it's more like the best 25 you can get together."