Maradona also apologised on Facebook for smoking a cigar on Saturday, despite a Federation Internationale de Football Association ban on smoking at World Cup stadiums.
There were tight affairs before a thrilling match between Spain and Portugal.
True to form, Iceland fought back and Finnbogason netted the equaliser four minutes later, pouncing when Argentine keeper Wilfredo Caballero parried away Gylfi Sigurdsson's shot for a classic poacher's goal.
He also missed a late free kick, unlike the Portuguese, and where Ronaldo's speculative shot had squirmed under the Spanish goalkeeper, Messi's efforts flew wide of the Icelandic goal.
Argentina's forward Lionel Messi runs with the ball during the Russian Federation 2018 World CupGroup D football match between Argentina and Iceland at the Spartak Stadium in Moscow on June 16, 2018.
Argentina legend Diego Maradona has denied making a racist gesture toward South Korean fans at his country's World Cup game in Moscow on Saturday. It starts with France's game against Australia, while Group C rivals Peru and Denmark face off later in the day.
"It hurts me to have missed the penalty, because it was the decisive advantage", Messi said after the game.
At the end, Messi retreated alone into the center circle with his head bowed and hands on his knees.
In contrast, Messi, with the score at 1-1, drove his free-kick straight into the wall, booting the ball into the air in frustration as the final whistle sounded seconds later.
After surviving that scare, the thousands of Argentina fans who packed out the Spartak Stadium were dancing in the Moscow sunshine when Sergio Aguero put them ahead with a superb strike after 19 minutes.
This time, as many on social media pointed out, Maradona's infamous "hand of God" was holding a cigar in defiance of Fifa's no smoking rules.
"This result doesn't have to weigh on us looking forward".
Croatia beat Nigeria 2-0 in their opening game on Saturday while Argentina were held to a 1-1 draw by Iceland in what is one of the toughest groups in the tournament.
They share a group with Croatia, Argentina and Iceland, so the odds are never in their favor.
Stunned Germany hopes to avoid early World Cup exit
To defeat the reigning world champions and many pundits' favorites to lift the trophy again was special enough. Mexico attacked often in the first half, creating a chance that perhaps Lozano should have converted early on.