Paul Pogba gave away a penalty, scored by Robbie Brady, to see Les Bleus fall 1-0 behind just two minutes after kick-off in the round of 16 at Stade de Lyon.
Head coach Didier Deschamps took off N'Golo Kante and sent on Kingsley Coman at the break, changing from a 4-3-3 formation to a 4-2-3-1 and sparking a comeback which saw Griezmann net both goals in a 2-1 win.
Asked about the team's latest problems in the first 45 minutes, a recurring theme for the hosts at the European Championship, Rami said: "This is the case since the start of the Euro. It's hard to start our matches.
"The good thing to remember is that we are mentally strong. If that's enough to take us to the final, why not? But I think it will be difficult.
"At 1-0, sincerely we were afraid and we had trouble. But it was impossible that [we would be] going home now."
And it was not just in the final third where the effects of Deschamps' decisive changes were felt.
"We played with more possession," Rami said when asked about the much-needed alteration to the team's approach.
"It allowed me and [centre-back partner Laurent] Koscielny to be further apart.
"The game [could breathe] and [we] had Griezmann [in] his true position ... it is very hard to stop him. He was lovely and could even have scored a hat trick."
"I knew I was in the red before the game," he said, referring to the risk of incurring a ban.
"But we have no time to calculate [our decisions]. The most important thing is to take France into the quarter-finals.
"The qualification gives me pleasure. There were 23 selected players [in the squad] and I trust everyone."