Rafael was booed by Brazilian fans at Wembley after his blunder led to Mexico striker Oribe Peralta's opening goal after just 30 seconds.
The Manchester United right-back dwelt on the ball too long and then played a poor pass that was intercepted in the build-up to Peralta's strike, and Rafael compounded a miserable performance by arguing with team-mate Juan following another mistake in the closing stages.
But Menezes is adamant the 22-year-old's error was not the only reason for Brazil's defeat and he claimed the whole team should shoulder the blame for failing to respond to that early setback.
"We have that national culture [of finding a scapegoat] when things don't go well and you are not going to change it overnight," Menezes said.
"Individual mistakes were made and the major one was made at 30 seconds today, but we had 89 minutes to turn it around and we didn't manage to, so we all lost, not just one player.
"On previous occasions we were able to deliver after going behind but this time it wasn't possible. Unfortunately we weren't able to react as we should have after our accident in the first minute. We didn't improvise or change our tactics.
"But our opponents were extremely well prepared. We acknowledge they were the better team and we congratulate them on their victory."