Messi, who is shouldering enormous pressure to succeed in what could be his last World Cup, failed to run through the gauntlet which was laid down by rival Cristiano Ronaldo - who managed to score a hat-trick against Spain on Friday night.
Argetina were, however, presented with the flawless opportunity to restore their advantage in the 64th minute when Maximiliano Meza fell under a challenge from Hoerdur Magnusson seven yards from goal.
"We've worked to see if we can limit their advantage" in the air, he said.
The Argentina great, considered by many to be the best player of all time, has missed more than 20 penalty kicks in his career. He watched in horror as his 88th spot-kick in the 2002 group game against Sweden was saved by Magnus Hedman, only for Hernán Crespo to save the day by tucking in the follow-up to earn the Albiceleste a draw.
The Argentinian was spotted in the stands watching his countrymen take on Iceland at the group D tie at the Sparatak Stadium in Moscow. "We are a country that puts everything into football and I'm sure we'll have 40 million people following us tomorrow".
For anyone who has ever missed a penalty at any level, there was some consolation on Saturday - Lionel Messi can miss them too.
Sergio Aguero gave his side a 19th-minute lead, but Iceland equalised less than five minutes later through Alfreð Finnbogason.
Griezmann's well-struck shot was the first VAR-awarded penalty at a World Cup.
While fans are thrilled to cheer on Lionel Messi in the 2018 World Cup, the Argentine athlete has revealed that he's unsure if this will be his last one.
And then there's Iceland's X-factor, what Icelanders call "Islenska geoveikin", which roughly translates as 'Icelandic madness.' On the pitch, the Viking mindset translates into a team that doesn't have the silky skills of World Cup glamour squads but likes to think it can outwork anyone.
"We're bluntly honest in our ability", coach Heimir Hallgrimsson said.
"We haven't lost hope because we drew, we'll continue on with the same desire to win".
Croatia face Argentina in their second group game. We're going to go out there to beat Croatia.
"To evaluate and characterise Lionel Messi's work is hard because it was an uncomfortable match for him", Sampaoli said.