The Premier League outfit are preparing for friendlies with A-League sides Wellington Phoenix on Wednesday, and Sydney FC on Saturday.
The Londoners finished 13th in the English top flight in 2013-14, having secured a top-10 placing on their promotion season 12 months earlier.
And Allardyce said their fall was due to a lack of points picked up at Upton Park.
"I think it's all about winning, and winning the right way," Allardyce said.
"There's times when you play at home, where our big problem lay last year.
"Because if you play really well and lose, that doesn't make much difference to any fan across the board today.
"So it's about playing well, but it's about winning as well, and that's what we didn't do at home enough last season."
Allardyce said he was looking to improve their fortunes, after an uplifting 10th placing in the 2012-13 season.
"I'm not totally convinced that all the hype on changing the way West Ham play really is the key element," he said.
"The key element is it was producing what we did the year before, and try to be better and we didn't do that.
"And I think when that didn't happen, we built such a big expectation in year one back in the Barclays Premier League that everybody expected us to push on and be better and greater in the next season, and that wasn't the case for various reasons."
Captain Kevin Nolan attributed their failure to climb the table down to injuries, claiming his personal output - seven goals in 33 games - was affected by forced rotations.
"I think that was a major thing for us last year, it was a lot of injuries," Nolan said.
"It was very difficult from me, from my personal point of view, to build up a relationship with a striker because we had a lot of chopping and changing to do because of the injury state [of affairs], what we had to put up with last year.
"So I'm really confident this year if we can stay away from them injuries, if we can keep Andy [Carroll] fit, as well as the signings… what I've seen of [Mauro] Zarate, he's a fantastic player, and someone I can certainly feed off to get goals, and someone who's going to score goals."
Carroll was kept to just 15 league appearances, scoring twice, but the former Newcastle striker said Allardyce was not overloading him with pressure yet.
"There's not that much pressure off the gaffer, he doesn't get on your back as much as he could have last season," Carroll said.
"There's not that much pressure, I'm just looking forward to the season without any injuries."
