Slovakia coach Vladimir Weiss is bitterly disappointed that his side gave up a 1-0 lead in the 93rd minute, allowing New Zealand to equalise and claim a point.
The Fighting Jondas took the lead in the 50th minute via Robert Vittek, but a Winston Reid header in the final minute allowed the All Whites to share the spoils.
"Of course it is a sad mood and we know it's part of football," Weiss told Goal.com.
"We train hard not to make mistakes but it happened.
"We just have to prepare for the next game. I hope that mistake doesn't happen again."
All four teams in Group F are on one point each after the opening round of fixtures.
How will Group F go? Check out Castrol Football's 2010 FIFA World Cup Group Predictor.