Allardyce has guided West Ham to seventh in the table after winning four of their opening eight league fixtures and will be looking to add to that when they face Wigan at the DW Stadium on Saturday.
Even though the Hammers were promoted through the play-offs last season they have accrued double the points of the other two sides who moved up from the npower Championship - Reading and QPR - combined.
But Allardyce believes the groundwork for such an impressive start was laid in pre-season.
"We knew that we had to hit the ground running," he said.
"I am not overly surprised about it because we worked hard in the summer. I think that the effort was put in by the staff then, by making the players aware that we have to be spot-on from game one, in terms of the level of our fitness, particularly our match fitness.
"Tactically we have to be right too, and start in the league as best as we can, with a group of fixtures that were quite good to us."
Former Blackburn boss Allardyce also feels it helped to avoid any of the so-called bigger top-flight sides in the early weeks.
He said: "Every game is difficult but in our first eight fixtures we only had Arsenal who are in the top four or top six on a regular basis. So that was relatively kind to us. But we have taken full advantage of our opportunities.
"There has only been one real disappointing performance in the eight - that was Swansea away. Even though we lost to Arsenal, I thought the performance was still good against a team as good as they were.
"The rest of the performances have been excellent, followed by some excellent results as well."
Most newly-promoted sides aim to simply survive in their first season in the top flight but Allardyce reckons his team are more than good enough to push further up the table.
"We never saw it as a relegation battle from the start," he said.
"It's about trying to finish as high up the table as we possibly can.
"The players all know what we have to do to get to where we want to go - at the first time of asking, that is around mid-table.
"That's our target. The target wasn't to finish fourth from bottom. The target was to finish in mid-table if possible. Of course, at the end of the day, survival is the ultimate, it's first and foremost, but if we can do better than that in year one then that would be great."
Despite the encouraging start to the campaign Allardyce is not planning on altering those targets in the knowledge West Ham now enter a period of difficult fixtures.
When asked if his season's target had altered, Allardyce said: "No, not really. We have had an excellent start but we look at the next few fixtures that are coming along.
"Wigan, Man City, Man United, Chelsea, Newcastle, Stoke, all those games together, and Liverpool - and this makes this group of fixtures extremely difficult to get more points.
"I don't think the target has shifted. What we have is a nice cushion of points that we have gathered in the first eight games. If things get a little bit tighter in the next fixtures, which they might do because of the size of the teams that we are playing, then we will still have had a nice cushion to stay in and around the top half or middle of the table, which will be very important going into Christmas."
West Ham travel to face Wigan on Saturday with the Latics yet to record a league victory at home this season.
But Allardyce expects a tough challenge from the side who thrashed West Ham 4-1 in the Capital One Cup earlier in the season.
"I was glad that we got our first three points away from home against QPR - which followed the draw at Norwich," Allardyce said.
"We have to look to increase the points total with a positive result - whether that is a draw or a win. We are hoping for a win but if we come away with something then we will be delighted from our point of view."