The Kiwis won the Oceania qualifying group by seven points, but then had to wait 11 months to play an intercontinental play-off against Bahrain, who finished fifth in Asian qualifying.
The play-off system looks set to come under intense scrutiny by FIFA after Thierry Henry's infamous handball which helped France eliminate the Republic of Ireland in Paris, and Nelsen is all for changes to be made.
"I never have been a big fan of them (the play-offs)" Nelsen said.
"There is so much on the line for one or two games and in the end, it generally falls into one situation where it's a handball or something like that.
"Over a league or a table, generally one instance like that doesn't affect the outcome."
Asked whether he would like to see FIFA get rid of the play-offs altogether, the Blackburn defender said: "I'd love it. That's our problem in New Zealand - we wanted to have a tougher group so that we could play a certain number of games.
"We came into this home and away match against Bahrain with no preparation at all. Bahrain had played 18 or 19 games so they were hardened to it, where we were just running on adrenaline really.
"We would love to have that scenario - it would take out all the controversy I think and obviously a team like Ireland would as well. You feel bad for them, but that's sport I suppose."