The team ranked 43rd in the world are seen as outsiders in their pool despite being one place above Nigeria, against whom they drew a blank against in Curitiba, in the world rankings.
It will only get harder for Carlos Queiroz's team as they next face Argentina, one of the favourites to win the tournament, and Bosnia-Herzegovina, who boast a number of players from top European clubs.
"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," said Nekounam.
"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.
"We could have snatched a win in the last 20 minutes but we lacked the finishing touch - I think that's the area we need to improve in.
"But when you consider that a lot of our players were making their World Cup debuts, it was a very good day for us."
Queiroz admits avoiding defeat in their opening game at least gives them some confidence ahead of the daunting task of facing Argentina on Saturday.
"We're relieved to have got the point. We're up against Argentina in our next game and if we'd lost this match, then we would have left ourselves in a very tricky situation," he said.
"We are very happy because Iran have got much less to work with than other sides.
"The most important thing we can take from this game is that our morale is high. It's shown that we can get results."