Vinicius Junior pounced on a defensive error to put Brazil ahead in Miami and scored again before half-time, with Matheus Cunha completing the job in the second half.
The result left Scotland in third place in Group C behind Brazil and second-placed Morocco with three points, leaving them to cling to the slim hope that they can qualify as one of the eight best third-placed teams in the 48-team tournament.
"We fell short on quality tonight, but we gave it absolutely everything," McGinn told the BBC.
"The lads are empty now," he added. "We've given ourselves a more difficult chance. It's unlikely now, I would say, but we'll wait and see."
Reflecting on the defensive blunder by Scott McKenna that led to Vinicius' opening goal for Brazil, McGinn said: "This is the top level, and if you make mistakes you get punished.
"We know we have to be better, but we just need to wait and see now."
The Aston Villa man paid tribute to the huge army of Scottish supporters, who have turned Boston and then Miami into a giant party.
"It's a bit raw at the minute, but we appreciate the support of the fans," he said.
"We know how difficult it is to be here, and hopefully the journey's not over, but they've been absolutely outstanding, and if we have to go again, we'll go again."
World Cup 2026
The 2026 World Cup will be held from June 11th to July 19th in the United States, Canada and Mexico. The tournament will feature 48 national teams and will be played in 16 modern stadiums.
Match schedule and times | Group tables | England at the World Cup | Scotland at the World Cup | Team rosters at the World Cup | How to watch the World Cup | Predictions and odds | Which teams could be considered dark horses?