Sergio Aguero sent Argentina ahead in the 19th minute, but Iceland were level four minutes later through Alfred Finnbogason, and that was where the scoring ended on Saturday afternoon as the points were shared.
Next up for Argentina in Group D is a clash with Croatia on Thursday night, and Mascherano has called on the South American nation's supporters to stay behind their team.
"It's not the best feeling. We wanted to win, we tried everything and we could not. It's never easy to play the first game, but you have to keep going," Mascherano told reporters.
"This is just beginning, it's not allowed to fall, but it has not been our day. We knew of the difficulty with a rival who defends with people back, very close. We made it all uphill, we thank the fans and we ask them to continue supporting us. We are going to need them."
Lionel Messi also missed a second-half penalty for Argentina in the entertaining affair with an Iceland side competing in their first ever World Cup.