Inter Miami remain winless at their new Nu Stadium after Saturday’s 2-2 draw with the New York Red Bulls.
Jorge Rucalvaba put the visitors ahead after 15 minutes, but Inter Miami hit back, with Mateo Silvetti levelling just before the break.
That advantage lasted only ten minutes after the restart, however, as Adri Mehmeti earned a point for the visitors in the closing stages.
Messi almost won it with a late free-kick, and Luis Suárez came off the bench in the dying minutes.
Inter Miami remain third in the MLS Eastern Conference on 12 points from seven games, four adrift of leaders Nashville.
Manager Javier Mascherano felt his side deserved more. “The mistakes we made proved costly, but the players gave their all to win today.”
Meanwhile, Pascal Jansen’s New York City FC missed out on second place in the MLS as Vancouver Whitecaps proved too strong, winning 2-0. The New York side sit fourth, one point behind Inter Miami.