Argentina’s opening match at Russia 2018 ended in a 1-1 draw in Moscow after Alfred Finnbogason’s historic goal cancelled out Sergio Aguero’s opener in Saturday’s Group D meeting.
Messi was denied by Hannes Thor Halldorsson when he took a second-half spot-kick - and he recorded 11 shots in the game without beating Iceland’s goalkeeper.
Argentina’s captain, a three-time beaten finalist at major tournaments with his country since 2014, does not want to panic after Iceland claimed a major scalp on their World Cup bow.
“It was hard for us to break, it’s not easy when a rival plays so far back,” Messi told reporters.
“The penalty was painful, I feel responsible.
“We do not have to go crazy, we deserved to win, but we have to improve a lot, now we have to be calm.”
Barcelona superstar Messi has now failed to convert four of his last seven penalties for club and country.
But the 30-year-old is ready to look ahead to Argentina’s next match, against Croatia on Thursday.
“This is just beginning and we knew it would not be easy,” Messi said.
“It’s a bad fight because we deserved to win, we were superior to Iceland.
“We have things to improve, we’re going to beat Croatia.”