Allardyce, speaking alongside captain Kevin Nolan, Andy Carroll and Winston Reid, praised the traditional welcome from their hosts and spoke of their enthusiasm for their upcoming fixtures against Wellington Phoenix and Sydney FC.
"It's fantastic for us to travel and experience this part of the world," he told the club’s official website.
"We're all really looking forward to it and our pre-season is going to be enhanced not just by us taking a tour but also from a cultural point of view.
"Our welcome was fantastic. It's a tradition for New Zealand and we've all seen the Haka before, but we'd not seen the whole thing and had it explained to us as it was. It was very interesting and a great welcome from our point of view.
"We're all very much looking forward to seeing the sights of New Zealand, as well as playing football here and promoting West Ham and the Barclays Premier League worldwide."
West Ham’s 2013/14 campaign suffered under the strain of repeated injuries, and Allardyce is desperate for the team to remain fit through the tour and be ready for Tottenham on August 16.
For Reid and Carroll, the challenge of staying fit is one they are relishing after a 2013/14 season ruined by ankle and foot problems respectively.
"I was out for four months and I came back into the team but it was a little hard to get going again but I got there in the end," said Reid.
"It will be nice to get another full pre-season under my belt. I'm just looking forward to a pre-season with no injures."
Carroll is equally determined to stay fit and show everyone exactly what he can do in a West Ham shirt.
"It's a very important pre-season for me after I had a very bad season last year with injuries. It's important I stay fit and do everything right with the medical staff."
West Ham face A-League sides Wellington Phoenix at Eden Park, Auckland on 23 July and Sydney FC at Westpac Stadium, Wellington on 26 July.