The 30-year-old Barcelona star’s second-half spot-kick was easily stopped by opposition keeper Hannes Halldorsson with the score at 1-1.
Messi was looking to match the impact his old rival Cristiano Ronaldo has made so far with a sensational hat-trick against Spain on Friday night.
“It would have changed the script. It was the advantage,” he said.
“Obviously it hurts me to have missed the penalty. They would have opened a little more and we could have found more spaces.
“We have the bitterness of not being able to take the three points that we deserved. To start with winning is always important, now we have to think about Croatia.
“We will try to pass this quickly. ”
Messi said Iceland’s tactic’s made it hard for his side claiming “they did not want to play” but admitted that Heimir Hallgrimsson’s team “closed well”.