A late goal by Bernardo Silva got holders City over the line although they rode their luck against a Chelsea side who were punished for not taking the numerous chances they created.
City, who were without fatigued striker Erling Haaland, lacked their usual zip and, despite reaching another final, Guardiola was clearly agitated at his side's lack of recovery time after the heartache of Wednesday's Champions League exit.
"It's unacceptable to let us play today," Guardiola said. "It's impossible, for the health of the players. It's not normal. It's unacceptable. 120 minutes, the emotions of Madrid, the way we lose, honestly.
"I know this country is special (with the FA Cup) but it's for the health of the players. I don't understand how we survived today."
Guardiola could not fathom why City's game against Chelsea was not scheduled for Sunday rather than Manchester United's semi-final clash with second-tier Coventry City, neither of whom had to play a match in midweek.
"The only power I have I say here. Why don't we play tomorrow? Chelsea, Manchester United, Coventry didn't play midweek," Guardiola said.
"Mentally so tough to recover. Rodri, the way he played today, Kyle (Walker), who was injured for a few weeks, I don't understand how they survived.
"We want to play football, we love to play football, but it's too much. We defend our trophy. We'll be here."
The exit to Real ended City's hopes of a second straight treble, although they are still in the hunt for a Premier League/FA Cup double.
"We're happy with another final and another chance to win a trophy," Silva, who made amends for his miss in the penalty shootout, said.
"We've done it throughout the years many times. The way this team reacts to disappointments and defeats is always in the best way. Today again the team showed a lot of character."
