Messi and his former Barcelona teammate Jordi Alba both sat out the game with Martino saying it would have been "very reckless" for the Argentine to play in Atlanta.
Martino said that his focus was on having his team ready for the U.S. Open Cup on Sept. 27 when Miami hosts Houston as in its bid for a second trophy of the season.
"They will train tomorrow [Sunday] and we will see day by day. Nothing changes our outlook on how he [Messi] will train. We have no urgency," said Martino.
The Herons face Toronto FC, the only team below them in the Eastern Conference, at home in MLS action on Wednesday.
"If he is well and confident he can get to play and if this doesn't happen he will wait a few more days," Martino said.
Miami's loss was the first in 12 games in all competitions since Messi and Spanish pair Alba and Sergio Busquetsjoined the team in July.
The defeat makes it tougher for Miami to climb into the top nine in the Eastern Conference. In 2023, MLS expanded the playoff fields for seven to nine teams.
"This defeat hurts us and reduces our chances but it is not decisive," said Martino, who said the U.S. Open Cup remains a priority. "The final is one game. It's very tempting to go for a title. We started the race very far back, we are not going to abandon it but our sights are set on the (Open Cup final on the) 27th," he said.
The 36-year-old Messi had also sat out Argentina's World Cup qualifier against Bolivia in La Paz on Tuesday, but he travelled and watched his teammates from the bench.
© Agence France-Presse