Carlos Queiroz's men opened their FIFA World Cup campaign with a goalless draw in Curitiba on Monday - the first stalemate in 14 games thus far in Brazil.
The result further highlighted Iran's defensive capabilities, having kept their fourth clean sheet in five competitive games.
But while Nekounam was pleased to have claimed a point, the 33-year-old midfielder said his team-mates must improve in the attacking third after scoring just four goals in five matches in the lead up to the World Cup.
"We could have snatched a win in the last 20 minutes, but we lacked the finishing touch," Nekounam told FIFA.com post-game at the Estadio Joaquim Americo Guimaraes.
"I think that's the area we need to improve in. When you consider that a lot of our players were making their World Cup debuts, it's been a very good day for us."
Nekounam added: "We knew it wasn't going to be easy at all and we also knew that we'd lose if we didn't keep our focus.
"We are happier with the result than they are, but we can't just settle for what we've got.
"We only have one point and we still have two very difficult games ahead of us."
Iran are back in action against South American powerhouses Argentina on Saturday before facing Bosnia-Herzegovina four days later
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